A galaxy group is a smaller grouping than a galaxy cluster, usually consisting of 50 or fewer large galaxies and the several hundred various dwarf galaxies orbiting them. Some of them are very compact, with galaxies so close that they interact with each other regularly.
They can be grouped together into galaxy clusters or superclusters. There are likely millions or billions of galaxy groups in our universe alone.
Our own local group is a very small galaxy group consisting of the Milky Way, the Andromeda Galaxy, and the Triangulum Galaxy, along with their dozens of dwarf galaxies.