Are you familiar with the following result?
is a homomorphism with kernel
and is onto, then
This is the theorem that Swlabr is suggesting you should use to solve your problem.
@ Swlabr, tonio
The term “first isomorphism theorem” is not a standard one in the literature of group theory. Different books call the result above by different names. In A Course in Group Theory by John F. Humphreys, for example, the author refers to this result as the Homomorphism Theorem (reserving the term First Isomorphism Theorem for a different result). Most likely Haven’s book does not call the theorem above the First Isomorphism Theorem either. Instead of beating about the bush, it might have been more helpful to Haven if you had just stated the theorem explicitly, as I have done.