(group of fifty or fewer gravitationally-bound Milky-Way-sized galaxies)
A galaxy group (or group of galaxies or GrG)
is a group of (on the order of) fifty or fewer "significant" galaxies
(e.g., with the luminosity of the Milky Way or brighter)
that are gravitationally bound, perhaps along with some
smaller galaxies, e.g., dwarf galaxies.
(Another criteria is that a galaxy group is a group of galaxies
with a total mass of less than 1014solar masses.)
The Milky Way is within such a group termed the Local Group.
A galaxy group can be part of a galaxy cluster.
A compact group is a galaxy group within a small volume.
A loose group is the other extreme.
The term subgroup (for galaxy subgroup) is definitely used
within the Local Group, essentially meaning a significant galaxy
plus its satellite galaxies, but likely is sometimes based
upon mere proximity. An example is the Milky Way subgroup.