SPWeb has two sharepoint cross-site group collection, SPWeb.Groups and SPWeb.SiteGroups.

SPWeb.Groups returns collection of cross-site groups which has some permission on the site. So if you add group from a site without any permission on the site, then this group wont appear in SPWeb.Groups collection, but it will appear in SPWeb.SiteGroups collection.

You can not use SPWeb.Groups.Add method to add new cross-site group, you need to use SPWeb.SiteGroup.Add method for this purpose.

In addition to this SPWeb has a property AssociatedOwnerGroup, which will return the required SPGroup. You can iterate the SPGroup users to get the list of all owners of the site.

 foreach (SPUser user in web.AssociatedOwnerGroup.Users)
 {
      // .. list all the users                        
 }

Finding and adding group

SPGroup  group = GetSiteGroup(web, "groupName");
if (null == group)
{
 web.SiteGroups.Add("groupName", web.AssociatedOwnerGroup, null, "Test Group description");
}

private static SPGroup GetSiteGroup(SPWeb web, string name)
{
    foreach (SPGroup group in web.SiteGroups)
    {
 if (group.Name.ToLower() == name.ToLower())
 {
     return group;
 }
    }
 return null;
}