I think the best word to use here would be Cineal or Cenel meaning "children of" or "offspring." For example the O'Boyles were a tribe of Cineal Conaill, descendents of Connal Gulban. Cineal Conaill were a "sub-tribe" or branch of the Northern O'Neill. O'Neill being the main chief. This could be compared to (as mentioned earlier) to the MacDonalds being a branch of Clan Donald.