What are all the homomorphic images of D3 (up to isomorphism)?
the kernel of such homomorphism is a normal subgroup of $\displaystyle D_3.$ now $\displaystyle D_3$ has only 3 normal subgroups: $\displaystyle (1), D_3,$ and a subgroup of order 3. so the homomorphic images are $\displaystyle (1), \ D_3$ and $\displaystyle \mathbb{Z}/2\mathbb{Z}.$