Number of orbits of projective action

Question

let $L/K$ be a finite field extension (if you want, assume $K=\mathbf Q_p$). Do we know the number of orbits of the action of ${\rm GL}_2(K)$ on the projective line $\mathbf P^1 (L)$ ? If $L/K$ is quadratic, then it is obviously $2$. What in general ?