quartering vs division

quartering and division both are nouns.

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

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

quartering (noun)	division (noun)
dividing into four equal parts	the act or process of dividing
living accommodations (especially those assigned to military personnel)	an arithmetic operation that is the inverse of multiplication; the quotient of two numbers is computed
a coat of arms that occupies one quarter of an escutcheon; combining four coats of arms on one shield usually represented intermarriages	the act of dividing or partitioning; separation by the creation of a boundary that divides or keeps apart
	one of the portions into which something is regarded as divided and which together constitute a whole
	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