Take a look at the SocialGroupBrowseFilterProvider, line 36. That's where the social group types are added to the BrowseFilter, which then passes this information on to be rendered in the SELECT element you mentioned. You could override the SocialGroupBrowseFilterProvider via spring.xml in your plugin, and add a condition there to skip adding the "secret" type if the current user isn't an admin.
Another way to do it would be to do overlay the soy file (/classes/soy/browse/filter.soy), and add your modifications in the template .compositeFilter, but I wouldn't recommend that, because you'd be overlaying quite a lot of other templates as well.
Would be nice though if the isVisibleToRegisteredUsers() in SecretSocialGroupTypeConfig would be honored when compiling the items for the select.
Thanks for pointing out the exact location where modification had to be done.
I tried overriding the SocialGroupBrowseFilterProvider and added a condition there to skip adding the "secret" type if the current user isn't an admin.
This worked and now getting the options in the SELECT as intended.
Thanks a lot for the help.