What term refers to a division or split into factions?

The term "schism" specifically refers to a division or split into factions, often used in the context of organizations, religions, or political groups. It denotes a significant separation that arises from differing beliefs or practices among members of a group. The notion of schism is important in understanding how groups can fracture when there are fundamental disagreements or conflicts of interest.

In contrast, the other terms do not carry the same meaning. "Satiate" relates to satisfying or fulfilling hunger or desires, "sanction" can refer to either a penalty or a formal approval, and "secular" pertains to things that are not religious or spiritual in nature. Therefore, the clear distinction and definition of "schism" as a term for division or split into factions makes it the correct choice in this context.