Something that's factional is broken into smaller parts. A government that's divided into opposing groups faces factional bickering that can make it hard to accomplish much of anything.
Factional comes from faction and its Latin root, factionem, "political party or class of people." Your huge family might be split into factions that are bitterly divided about where to go for dinner while on vacation, with nightly factional bickering over pizza versus seafood. Any group that includes smaller, highly opinionated groups within it can be described as factional.