How do cosets and Lagrange thm apply to this problem

From: Warren Chou (whchou_at_gmail.com)
Date: 03/05/05 

Date: 4 Mar 2005 16:00:59 -0800

Would appreciate any pointers on this question, especially on how
cosets and Lagrange's theorem apply here:

If G is a noncyclic group of order 27, then for how many elements x of
G do we have x^9=1?

Thanks,
Warren