schism

Short definition from Wiktionary

Noun

1. 1
   A split or separation within a group or organization, typically caused by discord.
2. 2
   A formal division or split within a religious body.
3. 3
   a split within Christianity whereby a group no longer recognizes the Bishop of Rome as the head of the Church, but shares essentially the same beliefs with the Church of Rome. In other words, a political split without the introduction of heresy.

Verb

1. 1
   To split, divide (a group or organization).