A Galaxy Group (or Group Of Galaxies or GrG) is a group of fifty or fewer "significant" galaxies (e.g., with the Luminosity (L) of the Milky Way or brighter) that are gravitationally bound, perhaps along with some smaller galaxies, e.g., dwarf galaxies. The Milky Way is in such a group named the Local Group (LG). A Galaxy Group can be part of a Galaxy Cluster (CL).
A Compact Group is a small group in a small area.
Galaxy Cluster (CL)
Local Group (LG)