I am trying to figure out all of the homomorphisms between these groups.
First by homomorphisms properties, the identity of $\Bbb Z_{24}$ is mapped to $\Bbb Z_{18}$ (i.e $\phi(0) = 0$).
After that, I got a bit confuse since the different combinations of mapping between the groups do not seems clear to me. I tried to list all of the subgroups of both groups but I do not know how these informations are helpful to me.
Thank you,