A factious group is one that breaks away, or wants to. It’s often used in politics, where people separate into smaller like-minded groups. The Confederacy was factious — they wanted out of the Union, but we know how that turned out.
The word factious looks a lot like its cousin faction, which is a small, sometimes rebellious group. Factious, then, is easy to remember, as the adjectival form of the noun faction. To be factious is to act like a faction. Among bakers, almost all agree that you have to be precise when measuring ingredients. The Brooklyn Faction, though, disagrees. This factious bunch never uses measuring cups or spoons and has called for them to be abolished.