The local group is an association of over 50 nearby galaxies.  Our Milky Way, M31 in constellation Andromeda and M33 in constellation Triangulum are the largest. The Magellenic Clouds are dwarf galaxies orbiting the the Milky Way. M32 and M110 orbit M31. Both the Milky Way and M31 have over a dozen known satellites. The rest are unstructured dwarfs, orbiting the group's common center-of-gravity.
The gravitational center of the local group lies between the Milky Way and M31. The entire group has a dumbbell shape about 10 million light-years in diameter. The local group is a member of the Virgo Supercluster which includes thousands of galaxies.