Ohhhh, information! Let's speculate:
Clan Angrund - Nobles - Small - K8PO - Karag Lhune
Royal Clan of Karak Eight Peaks.
We know that in this case, small means ~1000 from the armored rune-warriors during the reclamation. I'm going to bet these have almost all settled in Karag Lhune, are probably heavily involved in rebuilding the communities and public facilities to demonstrate their leadership making things better for eveyone, but have probably spent the last three years mostly as mediators and buffers between the Okrul and the K8P clans- as the royal clan of K8P, they have the authority to make participants in lesser disputes back down without dishonoring themselves. I'm betting there is going to be a strong tradition of judges and arbitrators in the future, as the first actual responsibility of ruling most of them got was trying to make two prideful groups get along. Practical ruling 101, but not the sort of thing that legends of good rulers tell about.
Also, given how they have been forced to play middledwarf between the true radicals and the old sticks-in-the-mud, I bet this pushes them more towards the radicals. They would have had a cultural affinity towards the old traditionalists, but I think having that group be the source of most of their headaches for years is a really good way to push them away from public affiliation with those viewpoints.
Clan Grimbrow - Nobles - Karag Rhyn
Settlers from Karak Izor, need new name
Decently sized (it was ~10,000 from Izor, across three clans, right? So probably at least 2,000) and with well-structured loyalties, with Princess Edda being both the figurehead for this group and the actual most-powerful member of it, on the K8P council. I'm betting that this clan is getting a lot more smelter and miner members since there isn't a foundation of other clans for them to be nobles over, being one of the largest single clans present, but I doubt they will drop the styling.
Rhyn was, as I recall, the final redoubt of the K8P greenskins before they were rolled up by the trolls, so even with the large number of members keeping the ecosystem suppressed is going to be a full-time job. I do expect this to keep the clan a bit removed from the other dwarves, allowing them to retain Izor cultural connections and traditions a bit more.
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Clan Huzkul - Warriors - Large - Citadel
Newly-founded clan of those that fought to reclaim Karak Eight Peaks.
The swol new guy of the dwarven clans, also about 10,000 members if I recall, and more than likely at least a minority settled in Lhune even if the citadel holds most. I'm guessing they low-key have a rivalry with the undumgi and the gunnery school as the other two warrior institutions with a history about as long as theirs. I think Dreng is the highest-ranking member as the K8P Military councilor, but he's not got much in the way of ties to clans or traditions- Huzkul might be the canary in the coalmine for civil strife, gathering a grab-bag of dwarves with likely very different (and potentially very extreme) views about traditions. If there is going to be a fight between traditionalists and radicals, look here where the 'don't shame us in front of the other clans' can be avoided by intra-clan fighting.
Also, this is very much going to be the poorest clan, and without much in the way of opportunity to build wealth as warriors. Long-term, this might be a problem, or it might just reinforce pre-existing social hierarchies as the noble and royal clans stay obviously richer.
Clan Helhein - Warriors - Karag Rhyn
Karak Norn skirmishers - crossbow warriors.
A middle-sized warrior clan, also in Rhyn, but not under the authority of the Grimbrow nobles. Interesting that they'd move out of Lhune- perhaps the is a 'young holds' attraction to grouping with the others in Rhyn?
Clan Stonebeard - Engineers and Pilots - Karag Lhune
Absorbed into Zhufbar, being refounded.
Gotri's clan, probably in the range of about 1,000 members if we assume that their numbers are equal to the total numbers of engineers in the expedition- the noncombat members balanced by the engineers in other clans. So, relatively small, high-prestige, and very much frustrated directly by the suppression of crafts in K8P. Probably live in the higher part of Lhune, near the gyrocopter hangers, and would be those rare dwarves accustomed to both sweeping vistas and stone over their heads.
On the other hand, Gorti is really the only representative of this clan that we actually know, and they stayed in Zuftbar while he was kicked out of there, so he's probably an outlier. But, he did lead them to victory and is the grandmaster of the guild here, so this clan is probably still the center of radical culture because the longbeards are going to be invested in defending him.
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Clan Bronzefists - Lode Wardens - K8PO - Karagril
Had a mountain in the Vault. Ironbreaker precursors.
First of the Karagil clans, not noted as exceptionally large or small, but we know that the garrison was ~3000 before the Calderabowl kicked off, so no more than a thousand, probably. This clan, along with Norgrimling, are probably the ones working closeest with Edda as she gets the silver mines explored and ready for production again. They took the first, and hardest, hit during the last battles, so are probably coming to see themselves as a vanguard for the K8P throng. Probably low-key super interested in finding gromril here again to restore their equipment.
Also probably suffering from an age of stolen hope mentality, where they did return to their ancestral home and conquer it, but they did so at a loss of many irreplacable members and the home they had built in exile. (as a side note, who do we think moved into their old mountain in the vault? A dwarfhold as free real estate can't be common.)
Clan Norgrimling - Miners - K8PO - Karagril
Ironbreakers in Zhufbar.
Very similar to Bronzefists, but likely to be slighty subordinate in practice as they were part of Zuftbar and the others had their own proto-hold. It would be interesting to see how they relate to Stonebeard.
Clan Ironback - Miners - K8PO - Karagril
Karak Azul deep-shaft miners.
And here we get the third part of the Karagil Krew, from Azul. We now have 'old' hold, 'new' hold, and isolated hold traditions all mingling in one mountain, where each clan actually fits the needs of the others quite well. Probably the most optimistic of the mini-meltingpots, since relying on others in a work situation seems like exactly the sort of thing you'd have dwarves do if you wanted to weld them closer to each other.
But these dwarves are also probably under a lot of pressure, as the only dedicated miners in a hold famous for silver and gromril, to start bringing up ore and prove out the long-term viability of K8P. Likely to be quite a lot of quite pride in being the only clan really doing what K8P dwarves are 'supposed' to be doing.
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Clan Irkokri - Masons - Karagril
Settlers from Karak Izor
Not much to say here, except that this clan was possibly the initial flashpoint with the Okrul what prompted them to be moved into their own baracks- I remember something about a dispute between the masons as the first call-out. It does strike me that they are trying to establish a bit more independence from Grimbrow, settling in Karagil while their former nobles settled in Rhyn, all the way across the caldera with the Huzkul as a buffer. Something might be going on there. Either way, sneaking suspicion that this clan is a trouble-maker/magnet.
Clan Stoneback - Masons - K8PO - Karagril
Grey and Black Mountains freelancers.
This seems like a clan that was on the verge of being absorbed into other holds, given 'freelancers', so I'm guessing their internal structure is weak and they are happy to follow Irkokri as they are similar in focus, origin, and probably traditions? Guessing this clan took on a lot of the contracts for dwarven work in above-ground areas, with lots of travel. Probably one of the best acclimated to above-ground living- so I'm guessing they are the leads on the aqueduct project.
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Clan Skorrun - Merchants - Small - Karag Rhyn
Settlers from Karak Izor
If this clan isn't doing it's best to get all the EIC contracts they can and serve as a middledwarf between the company and the other clans, I'll eat my hat. (Ok, so I don't have a hat, but the point stands.) This is a small clan with a huge opportunity, but from the way they chose to settle in Rhyn, it seems like they are more interested in the internal markets of the Karak and the Azul/Barak Var trade connections. Likely to have a charismatic leader- taking the gamble on settling a merchant clan in a frontier fortess is long odds, but getting the payoff of sitting on the best silk road route is the sort of payoff that would cement a leader's reputation.
I'm betting that if there is a dwarf liaison to Francesco as I suspect there is an EIC liaison, they are probably from this clan. Edda's people, so the steward would have thought of them first, and they would share most of the goals that the Undumgi and EIC are have w/r/t K8P.
Clan Dourback - Brewers - K8PO - Small - Karag Rhyn
Empire breweries
Brewers from the empire, a late addition and just getting set up. Ironically, this is the clan I see most likely to cause headaches to Mathilde in the course of her duties, because any elector count that had a dwarven brewery then lost it is likely to be a bit peeved.
Clan Ironspike - Carpenters - K8PO - Small - Karag Rhyn
Karak Hirn heavy-duty carpentry
Interestingly enough this clan is probably getting the most use out of the timber the ulrikadrin are cutting, and I bet the ones who built the shipyard came primarily from this clan. Possibly the dwarves the ulrikadrin are most exposed to- and also in heavy demand for scaffolding and temporary supports during the reopening of the mines. Demand is likely to drop off as Okrul leave and most of the work has replaced wood with stone or metal. Also with cannon being strongly favored over bolt throwers and catapults, so we'll see what areas they focus on in the future. Will they become contractors for ulrikadrin, primarily? Or will they expand into shipwrights, as Barak Var draws down it's staff as their dock expansion completes?
Clan Flintheart - Metalsmiths - K8PO - Small - Karag Mhonar
Barak Varr tinkers.
The only clan in Mhonar, and noted as 'small'. Also from Barak Var, so I don't think they were present for the reclamation, and are likely to have a bit of a younger sibling complex. Feel like they have to prove themselves, feeling a bit isolated in the giant echoing mountain, but looked at by the rest of the Karak as a proper and necessary group who fill exactly the need that K8P has. It's possible this leads to the smelters walking around with a bit of a chip on their shoulders.
So, overall, we've got two clans in Lhune (Agrund and Stonebeard), one small one in Mhonar, five in Rhyn, five in Karagil, and one in the citadel. It seems like there was a bit of an exodus from Lhune when reclamation finished, and now the three most populous areas would be Karagil, Citadel, and Rhyn.
Three mountains are still empty, so the Karag Kron might still be a go for Yar or Kvinn-Wyr, because I don't think the dwarves would be cool with Ziflin being given over: largest and proudest of the old peaks, even with a dragon in the penthouse and the rat's mess yet to be cleaned up.