。
She's one of the girls we invited to the party.
Literal
She [topic-は] we [subject-が] party [to-に] invited girls [among-の中の] one-person is.
Two structural points worth pulling apart. First, the relative clause 私達がパーティーに招いた modifies 女の子 — a clause-internal subject 私達が is marked with が (not は), since topical は is reserved for main clauses. Second, the partitive frame ~の中の一人 ('one of among~') is the standard way to single out one element from a known set: グループの中の一人 ('one of the group'), 友達の中の一人 ('one of my friends'). The plain noun + の repetition feels stiff in translation but is structurally clean and natural in Japanese.