I am no working on troubleshooting claims for Sitecore and Active Directory. Just want to share this admin-folder page that helps me seing the AD mapping.
1. Save this file from my GitHub into your admin folder under Sitecore:
https://github.com/MartinMiles/Sitecore.Pages/blob/master/sitecore/admin/AD-Groups.aspx
2. Run it in browser and the result will shop up as something as below:
