group vs regroup

group is a noun but regroup is not a noun.

Word	Noun	Adjective	Verb	Adverb
group	Yes	No	Yes	No
regroup	No	No	Yes	No

As verbs, regroup is a hyponym of group; that is, regroup is a word with a more specific, narrower meaning than group:

Other hyponyms of group include bracket, chunk, collocate, lump, batch.

group (noun)	regroup (noun)
any number of entities (members) considered as a unit
a set that is closed, associative, has an identity element and every element has an inverse
(chemistry) two or more atoms bound together as a single unit and forming part of a molecule

group (verb)	regroup (verb)
arrange into a group or groups	reorganize into new groups
form a group or group together	organize anew, as after a setback