According to the Kneser-Milnor prime decomposition theorem for 3-manifolds, any compact, connected, orientable 3-manifold $M$ is diffeomorphic to $S^3 / \Gamma_1$ # $\cdots$ # $S^3/ \Gamma_n$ # $(S^2 \times S^1)_1$ # $\cdots$ # $(S^2 \times S^1)_r$ # $K( \pi_1,1)$ # $\cdots$ # $K( \pi_m,1)$, where # is the connect sum, and $\Gamma_i$ is a non-trivial finite subgroup of $SO(4)$ acting orthogonally to $S^3$ (so that the result is a spherical space form).