We construct for each integer $n$ ($\geq 3$), infinitely many number fields of degree $n$ each of which has an unramified quadratic extension with a power integral basis but no normal integral basis.
"A note on unramified quadratic extensions over algebraic number fields." Proc. Japan Acad. Ser. A Math. Sci. 76 (5) 78 - 81, May 2000. https://doi.org/10.3792/pjaa.76.78