  We show that the homotopy type of a 4-manifold $M$ whose fundamental group is
a finitely presentable $PD_3$-group $\pi$ and with $w_1(M)=w_1(\pi)$ is
determined by $\pi$, $\pi_2(M)$, $k_1(M)$ and the equivariant intersection
pairing $\lambda_M$.
