"Department" is not a fixed term between US colleges and universities (much less international schools): it can be anything from a single professor with a shortlist of classes to dozens of professors within a larger college/school of humanities.

The very large state school that I went to had a classics department (and I took many courses in it), but it was probably only about half a dozen professors.

Besides: "Classics" is a difficult department to fit within another department. It usually already has a few sub-departments, ancient Latin and Greek among them.

Typically those getting a classics degree have to learn Greek and/or Latin. There simply is no substitute for reading in the original language. A ton is lost in translation.