Other forms: schisms
The sound of the word schism reminds some people of the sound of a piece of paper being torn in two; which makes sense — when a group has a big fight and the group is torn in two, that's a schism.
Although the Spanish club could have a schism over taco night versus tamale fest, schism often refers to splits in the church. You might have heard of the Great Schism of 1054, when the eastern Christian church, headquartered in Byzantium (now Istanbul), broke away from the western one headquartered in Rome.