The Milky Way is itself a galaxy. It does not belong to a galaxy, but to a galaxy cluster known as the Local Group. The Local Group is composed of over 30 galaxies including the Milky Way, the Andromeda Galaxy, the Triangulum Galaxy and several dwarf and irregular galaxies.
The Local Group, in turn, belongs to a supercluster known as the Local Supercluster. NASA describes the Milky Way as a typical galaxy. It is made up of hundreds of billions of stars, vast clouds of gas and dust, and dark matter held together by gravity. It also has a spiral shape like more than two-thirds of all known galaxies.