When you map a Google Site to your own domain, you first create a CNAME record in your domain registrar's control panel. Mapping must be to a subdomain. The common subdomain is "www'. So to map your site to that subdomain you create a CNAME record of type www that points to ghs.googlehosted.com. You then add your web address to your site. See this article. Note that you can add up to 5 URLs to one Google site. If you have published the site to only a specific group of people the custom URL will redirect to the sites.google.com URL.
You can create other subdomains in your domain control panel. These subdomains can point any site that you have created. See the examples below.
I have three custom URLs for this site:
www.k8oms.net, web.k8oms,net and new.k8oms.net
Thus there are 2 urls left for this site.
Multiple sites can be mapped to different subdomains of the same domain such as:
This is done by creating CNAME records in your domain control panel and adding the URLs to the various sites. There is no limit to the number of these CNAME records unless your domain registrar sets one.