Finite field extensions as projective group algebras

Question

For a finite field extension $K \subset L$, can $L$ always be seen as a projective group algebra over $K$? That is, does there always exist a finite group $G$ and isomorphism $L \simeq K _\alpha [G]$, where $\alpha:G \times G \to K$ is a twisting operation such that $g \cdot g' = \alpha(g,g') gg'$?