What you want then is a layer 3 "managed" switch.

You can create Vlan's on that switch which will let you separate your departments like you want.

Switches like these:
http://www.cdw.com/shop/search/resul...tBy=TopSellers

Would accomplish what you want..I'm partial to Cisco Switches.

But from the console of that switch you'll be able to create your Vlan's which will let you keep department traffic separate while still allowing access to the internet.

For example, you can configure physical ports 1-10 to be Network A with IP a.a.a.a
While Ports 11 - 24 are network B with IP b.b.b.b. You can apply custom ACL's to those Vlan rules to actually keep the traffic separate while using 1 router.