Threefolds of Order One in the Six-Quadric

Consider the smooth quadric $Q_6$ in $\mathbb P^7$. The middle homology group $H_6(Q_6,\mathbb Z)$ is isomorphic to $\mathbb Z\oplus\mathbb Z$, with a basis given by two classes of linear subspaces. We classify all threefolds of bidegree $(1,p)$ inside $Q_6$.