Group Theory: Describe all homomorphisms from Z to Z12

The kernel of φ must be a subgroup of Z, but doesn't Z have several subgroups? Not sure where to begin

Let φ: Z ---> Z12 be a group homomorphism.

Since Z is cyclic, φ is uniquely determined by φ(1), because φ(n) = n φ(1).
Since Z12 has 12 elements, there are 12 possibilities for φ(1); each of which yields a homomorphism.

I hope this helps!