headquarters vs military group

headquarters and military group both are nouns.

Word	Noun	Adjective	Verb	Adverb
headquarters	Yes	No	No	No
military group	Yes	No	No	No

As nouns, military group is a hypernym of headquarters; that is, military group is a word with a broader meaning than headquarters:

headquarters: (plural) a military unit consisting of a commander and the headquarters staff
military group: a unit that is part of some military service

Other hypernyms of headquarters include force, military force, military unit.

headquarters (noun)	military group (noun)
the military installation from which a commander performs the functions of command	a unit that is part of some military service
(usually plural) the office that serves as the administrative center of an enterprise
(plural) a military unit consisting of a commander and the headquarters staff