  When ordered by discriminant, it is known that about 83% of quartic fields
over Q have associated Galois group S_4, while the remaining 17% have Galois
group D_4. We study these proportions over a general number field F. We find
that asymptotically 100% of quadratic number fields have more D_4 extensions
than S_4 and that the ratio between the number of D_4 and S_4 quartic
extensions is biased arbitrarily in favor of D_4 extensions. Under GRH, we give
a lower bound that holds for general number fields.
