Hi Aiden,
This is what I tested and it worked for me.
SAtyaGrp3(local group)->SatyaGrp2(local group)->SatyaGrp1(local group)->Satyajit(GAL contact)
Sent email to SatyaGrp3, which worked.
Let me know, if you are doing anything differently. What is the error you are getting
If you are migrating the data from a older outlook to Outlook2013 it might have some issues it appears.
References:
Combine or nest multiple Contact Groups into one
http://www.msoutlook.info/question/860
Outlook 2013 - Combining contact groups
https://kb.niu.edu/page.php?id=49471