There is no advantage at all. ThreadGroups are there for backward compatibility, but I've never seen them used.
Here's what Brian Goetz (author of Java Concurrency in Practice - the bible) said about them a long time ago:
The ThreadGroup class was originally intended to be useful in
structuring collectionsof threads into groups. However, it turns out
that ThreadGroup is not all that useful. You are better off simply
using the equivalent methods in Thread. ThreadGroup does offer one
useful feature not (yet) present in Thread: the uncaughtException()
method. When a thread within a thread group exits becauseit threw an
uncaught exception, the ThreadGroup.uncaughtException() method
is called. This gives you an opportunity to shut down the system, write
a message to a log file, or restart a failed service.
Threads now have an uncauht exception handler, and this single reason to use thread groups isn't valid anymore.