Non-Abelian number field

An algebraic number field with a non-Abelian Galois group over the field of rational numbers $\mathbf Q$, or a field that is not normal over $\mathbf Q$. Sometimes, instead of $\mathbf Q$, one considers some other ground field $k$ of algebraic numbers, and the term "non-Abelian" is understood to refer to the Galois group over $k$.