A network management apparatus includes a first storage unit, a second storage unit, and a controller. The first storage unit stores therein communication groups included in the same subnet and information about communication devices belonging to the respective communication groups in association with each other. The second storage unit stores therein for each of the communication devices a port of a relaying device connected to the communication device as a connection destination port. The controller allows the relaying devices to perform communication between the connection destination ports on the basis of the first storage unit and the second storage unit to allow communication only between the communication devices belonging to the same communication group.