Let be a finite, normal extension of Q for which |Gal(/Q)| = 8 and each nontrivial element of Gal(/Q) has order 2. Find the number of subfields of that have degree 4 over Q. (Hint: A group where every element squares to the identity is abelian (Exercise 25 in Section 3.1 of version 4 of the text).) (Possible hint: the subgroups of index in Z are its 1-dimensional sub Z -vector spaces.)