When counting people from 2 to 10, and 12,you don't use the ordinary numbers, you use a particular set of "numbers of people" that are more like group nouns, and use the genitive plural. - beirt bhuachaillí, triúr fear, ceathrar ban, cúigear cailíní, seisear páistí, seachtar múinteoirí, ochtar daltaí, naonúr feirmeoirí, deichniúr cócairí, dháréag dlíodóirí.

(Many of these words happen to be in declensions where the genitive plural is the same as the nominative plural, but technically, they are all using the genitive plural).