This question has an answer here but It's not clear to me. computing the orbits for a group action
So, I am asking it again.
Let G be the galois group of a field with 9 elementsover its subfield with 3 elements. Then the number of orbits for the action of G on the field with 9 elements is?
I want to ask which result in Galois theory should be used. I have studied galois theory but couldn't solve problems due to lack of time. SO, Assume knowledge of graduate text of galois theory while answering it and kindly provide a bit detailed reasoning.
I am really struck so I am asking . Thanks a lot for your help!!