Normal Subgroups of S3xS3: How to Find and Classify Them?

[ToffeeC]

Homework Statement

Find all the normal subgroups of S3xS3

Homework Equations

The Attempt at a Solution

I know that whenever N1 and N2 are are normal subgroups in S3, then N1xN2 is normal in S3xS3. The problem is that there might be normal subgroups in S3xS3 than those obtained this way. Is there a way to go and find them aside from brute force?

 

[ystael]

If $$H$$ is a subgroup of $$\mathfrak{S}_3 \times \mathfrak{S}_3$$, what do you get when you conjugate $$H$$ by elements of the subgroups $$\mathfrak{S}_3 \times 1$$ or $$1 \times \mathfrak{S}_3$$?