a group separating from a larger one

withdrawal

a group of people in a larger group (e.g. a political party) with different views, often ones that suit their own interests

group sharing a belief or cause

the smaller number or part (of a group)

an outnumbered group

(an instance of) a division of an organization (especially Church) into two or more groups

separation

a group of people united by (especially political or religious) beliefs or opinions

school of thought