Restore backup to different filegroup

Using Sql Server 2008R2.

I have a backup of a filegroup. Is it possible to restore this to a different file group (possibly even on a different database)?

I have tried

RESTORE DATABASE my_database
   FILEGROUP = 'newFileGroup'
   FROM DISK='C:restorebackupOfFileGroup.bak' 
   WITH RECOVERY

But get the following error:

Filegroup 'newFileGroup' cannot be restored because it does not exist in the backup set.

Is it possible to restore this to a different file group

No.

possibly even on a different database)

No.