cleavage vs division

cleavage and division both are nouns.

Word	Noun	Adjective	Verb	Adverb
cleavage	Yes	No	No	No
division	Yes	No	No	No

As nouns, division is a hypernym of cleavage; that is, division is a word with a broader meaning than cleavage:

cleavage (noun)	division (noun)
the act of cleaving or splitting	the act or process of dividing
the line formed by a groove between two parts (especially the separation between a woman's breasts)	an arithmetic operation that is the inverse of multiplication; the quotient of two numbers is computed
(embryology) the repeated division of a fertilised ovum	the act of dividing or partitioning; separation by the creation of a boundary that divides or keeps apart
the breaking of a chemical bond in a molecule resulting in smaller molecules	one of the portions into which something is regarded as divided and which together constitute a whole
the state of being split or cleft	discord that splits a group
	an army unit large enough to sustain combat
	a group of ships of similar type
	a unit of the United States Air Force usually comprising two or more wings
	an administrative unit in government or business
	(botany) taxonomic unit of plants corresponding to a phylum
	(biology) a group of organisms forming a subdivision of a larger category
	a league ranked by quality