Galois group of a polynomial

Hello.

I have to find a splitting field of the polynomial over and the galois group and all intermediate fields of the algebraic extension .

I found out, that is irreducible, the roots of are:

and that is a splitting field of .

Furthermore I find out, that the three homomorphisms

have order 2, so the galois group is isomorph to .

But now I don't know how to find the fixed fields, which belongs to the homomorphisms.

For example: Which fixed field belongs to the homomorphism ?

The definition says:

...and this don't help me, because I need a description of the fixed field like this: (with suitable ).

I hope, you can help me.

Bye,

Alex