There are overlaps in this organization, but networking is too large a component to simply be lumped under devices, as are file systems. Security is a cross-cutting issue that affects everything else. For example, AMD now makes processors that have built in encryption capabilities using the VIA Padlock technology.
Process management includes management of the processor (scheduling and concurrency) and the creation, control and deletion of processes that users and/or the system create. Memory management is concerned with the allocation and deallocation of the scarce memory resource and the associated problems of secondary memory and swapping. Device management is concerned with the way in which the operating system interfaces user and/or system processes with physical or virtual devices. File systems are the layers the provide a logical interface between processes and disk drives or other media that can be treated in a similar fashion. This could be everything from tape drives to network interfaces to serial ports depending on the operating system. Networking is concerned with interprocess communication which could be either on the same system or on a remote system. And security issues include authentication (are you allowed to be here?), access (are you allowed to do that?), threats (this could be a virus and dangerous) and protection (only a certain set of people should be allowed to see this).
Of course, all operating systems include applications that may or may not be unique: web servers and clients (browsers), mail servers and clients, editors, compilers, libraries, MP3 and video players and so on. These are not necessarily functions of the operating system, but they are key elements in the functionality of a computer system.