301.10H Applying the First Isomorphism Theorem 

The first isomorphism theorem helps us "whittle down" a homomorphism to discover an isomorphism within. It does this by giving us a normal subgroup of G (the kernel of the homomorphism) and also telling us what the factor group by that normal subgroup is (it's isomorphic to the image of the homomorphism). Here's an example using dihedral and symmetric groups.