To split up or divide.
Additional Information
This is a regular verb you can logically create based on words like "fissiparous" which means divisive, and "fissipation" which means division. The reasoning process based on other similar construction can come to the logic conclusion that the word "fissipate" can be used as a verb. Use in a sentence: The political party could run into a disagreement that would fissipate some of its members into two different political parties.