Hi lovesmath!

Do you have a definition for a normal subgroup handy?

I'll give one that is reasonably easy to apply to your problem:

Definition:A subgroup H of G is normal iff .

Can you apply that definition for H=N and G=K?

Basically it means checking each combination of elements g and h.

Since it is trivial if either g or h is the identity, there are only 3 cases to check.

Alternatively, there is also a proposition that you may have:

Proposition:The kernel of a homomorphism from G to G' is a normal subgroup of G.

If you can find such a homomorphism this is less work.