Correspondence Theorem for Normal Subgroups in Groups of Order 168

[tyrannosaurus]

Homework Statement

Show that if G is a group of order 168 that has a normal subgroup of order 4, then G has a normal subgroup of order 28.

Homework Equations

The Attempt at a Solution

Let H be a normal subgroup of order 4. Then |G/H|=42=2*3*7, so then G?N has a unique, and therefore normal Sylow 7-subgroup, let's call it K.
I was told to use the correspondence theorem, but I am not sure where it works in here. any ideas?

 

[jbunniii]

Why don't you start by stating what the correspondence theorem says? The result you are seeking is an immediate consequence.