Finding all ideals N of $Z_{12}$ and compute $Z_{12}/N$ in each case. I already find all the ideals N of $Z_{12}$.
Here's what I've  got:
Since ideals must be additive subgroups, by group theory we see that the possibilities are restricted to the cyclic additive subgroups,
$<0> = {0}$
$<1> = {0,1,2,3,4,5,6,7,8,9,10,11}$
$<2> = {0,2,4,6,8,10}$
$<3> = {0,3,6,9}$
$<4> = {0,4,8}$
And
$<6> = {0,6}$
Now, my problem is how can I compute for $Z_{12}/N$ in each case; that is, find a known ring to which the quotient ring is isomorphic.
Thank You in advance for the help!

You might find the third isomorphism theorem helpful here if you think of $\mathbb{Z}_{12}\cong \mathbb{Z}/12\mathbb{Z}$.
