Groups of Order 144: Abelian Groups Up to Isomorphism

[BurrowK]

I'm going insane. The question is:
List all abelian groups (up to isomorphism) of order 144.

There are 10 non-isomorphic groups of order 144 and I only have 9. Here they are:

Z2 X Z2 X Z2 X Z2 X Z3 X Z3
Z2 X Z2 X Z2 X Z2 X Z9
Z4 X Z2 X Z2 X Z3 X Z3
Z4 X Z2 X Z2 X Z9
Z8 X Z2 X Z3 X Z3
Z8 X Z2 X Z9
Z4 X Z4 X Z3 X Z3
Z4 X Z4 X Z9
Z16 X Z3 X Z3

(with the isomorphism being Z16 X Z9)

Anyone? Bueller?

 

[morphism]

(with the isomorphism being Z16 X Z9)

What do you mean by this statement? Z16 x Z9 gives a distinct isomorphism class - it's precisely the one you're missing.

 

[BurrowK]

Yeah, I realized that that counted towards the 10. It's the midst of finals so the brain's on the fritz. I was just going to take this post down, thanks though!