7.8, due March 30

Does everything in groups have a connection to something in rings?  I get so confused when they have the same notation or even names (kernel!).  I had a little bit of a hard time wrapping my head around all this in rings and now it's like I have to unwrap it and wrap it up again but this time in groups.  Another thing I noticed was that there is no Second Isomorphic Theorem For Groups.  I got a little caught up wondering why it wasn't included.  It must exist if there is a third one but was it just not important enough to make the book?  As far as the actual math goes, it all seemed straight forward until I got to the composite factors of G.  I don't even know where to start with those.