the help on the last post does seem to have helped me a lot atleast upto the point where i can understand the basics.

heres the next one, as usual any hints on how to approach the question would be greatly appreciated. i will attempt the questions with the hints

(1)

describe explicitly all homomorphisms

(2)

For each such homomorphism describe the semidirect product in terms of generators and relations.

(3) How many distinct isomorphism types of groups of the form are there?