# Math Help - Homomorphic images of D3.

1. ## Homomorphic images of D3.

What are all the homomorphic images of D3 (up to isomorphism)?

2. Originally Posted by o&apartyrock

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