The Milky Way galaxy is part of the Local Group, which is a small group of galaxies that includes the Andromeda Galaxy, the Triangulum Galaxy, and several smaller galaxies. The Local Group is part of the Virgo Supercluster, which is a large cluster of galaxies. The Virgo Supercluster is part of the Laniakea Supercluster, which is a larger cluster of galaxies that includes the Milky Way, the Andromeda Galaxy, and the Virgo Supercluster. The Laniakea Supercluster is thought to be the largest structure in the universe.
While the Milky Way does not orbit any single object, it is in orbit around the center of mass of the Local Group. The center of mass of the Local Group is located somewhere between the Milky Way and the Andromeda galaxies. The Milky Way completes one orbit around the center of the Local Group every 225 to 250 million years.