Restricted front-end access
Is the physical web server inside your network as well? As mcclaskiem mentioned,  check to see if the IP address is within the subnet of your network and then allow access that way.

You may want to have the web server listen on another hostname that's not accessible outside the network and allow access to that vhost unconditionally (but do that at the firewall level). The would be the securest way to allow access within your network without logging in. IP addresses can be spoofed with varying threat so I'd be wary of allowing anyone to authenticate via just an IP Address if your webserver is located off-premise.

Dealing with google auth on the "other side" would obviously require a plugin for people attempting to connect outside the network.  

Here's another thread for further reading.