Well, technically your half right. You ARE on a Class A
network...sorta. If you are on an internal network, the
network admin more than likely has a NAT system set up.
With that, the netadmin can have set up the internal IP's
separate from the outside world. Standard internal IP
addressing is either 10.x.x.x, 172.16.x.x, or 192.168.x.x.
Then, the netadmin uses whatever subnet needed...in this
case, you more than likely have a single subnet, aka ur
entire network on the same network.
Now, NAT comes in when you want to reach out to the
Internet. The NAT server, which is either an actual
server, your firewall, or a gateway router, takes your IP
of say 10.65.26.132 and translates that into an EXTERNAL
IP address...which may be 65.68.7.16. The reason to do
this is two-fold: one is so that way, you can use a
limited number of IP address for a much large group of
users; hense you may have 25 people on your internal
network, yet only two external IP address. The other
benefit is security, and a hacker won't be able to
identify which workstation or what IP setup is in use, due
to the external IP address.
Sorry its a lil lengthy, but thats the jist of it.