I would like to know what are all the real three dimensional Lie groups (simply connected) that can act transitively and locally freely on a compact three dimensional manifold?

This is equivalent to finding all the real three dimensional simply connected Lie groups $G$ having a discrete subgroup $\Gamma$ such that $G/\Gamma$ is compact?

Some known examples are: $\mathbb{R}^3$, $\mathbb{S}^3$, $\sf{SL}(2,\mathbb{R})$, and the Heisenberg group.