**Second Isomorphism Theorem**

Let *G* be a group. Let *S* be a subgroup of *G*, and let *N* be a normal subgroup of *G*. Then:

- The product
*SN*is a subgroup of*G*, - The intersection
*S*∩*N*is a normal subgroup of*S*, and - The quotient groups (
*SN*) /*N*and*S*/ (*S*∩*N*) are isomorphic.

Technically, it is not necessary for *N* to be a normal subgroup, as long as *S* is a subgroup of the normalizer of *N*. In this case, the intersection *S* ∩ *N* is not a normal subgroup of *G*, but it is still a normal subgroup of *S*.

Read more about this topic: Isomorphism Theorem, Groups, Statement of The Theorems

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