Added website with a subdomain on Mountain Lion server couldn't be found on other machines

Added website with a subdomain on Mountain Lion server couldn't be found
on other machines

My server is accessible via example.com and I want my website to be
accessed via sub.example.com. I added a website to Mountain Lion server
with domain name that's actually a subdomain; sub.example.com. I than
added a new host name to DNS service, so that the hostname sub.example.com
resolves to the IP address of the server (192.168.1.2).
Now, I can view the website sub.example.com on the server itself, but
other clients in the local network are not able to access the website.
The command nslookup sub.example.com has this result:
Server: 192.168.1.2
Address: 192.168.1.2#53
Name: sub.example.com
Address: 192.168.1.2
Did I configure the website correctly? What's going wrong?