The departments for the Ministry of Magic are as follows:

Department of International Cooperation
Misuse of Muggle Artifacts Office
Goblin Liason Office
Department of Regulation and Control of Magic
Department of Magical Games and Sports
Improper Use of Magic Office
Commitee on Experimental Charms
Accidental Magic Reversal Squad
Department of Magical Transportation
Department of Mysteries.

In addition there are the International Conferation of Wizards and the International Confederation of Warlocks.


If I remeber correctly most muggle governments are divided into a national government, a regional government- which covers a state or provence- and a local government- that usually includes a city and county government depending on what country you are talking about.