Department also and often translates as "viddilennya". "Fakul'tet" in english can be also a faculty.
When I was a student at the university, my faculty (факультет) had several departments (кафедр) under its supervision.
Also, "department" could be translated as - "відділ". It really depends on the context. The Duo team just didn't included other possible translations. It's ery frustrating... And not only these course, but many others have the same problems :-(