Find the subgroups of it and correspond them to the intermediate fields.
For instance, if you choose a generator of the above group as , then one of the subgroups of it is .
The reason why I choose the above generator (among them) is because 3 has order 6 in ( Meanwhile, 2 has order 3 in ).
Since , the corresponding intermediate field is .
I'll leave it to you to find the remaining subgroups of and their corresponding intermediate fields.