Let $ 1 \rightarrow N \rightarrow G \rightarrow Q \rightarrow 1$ be an exact
sequence of finitely presented groups where Q is infinite and not virtually
cyclic, and is the fundamental group of some closed 3-manifold.

If G is Kaehler, we show that Q is either the 3-dimensional Heisenberg group
or the fundamental group of the Cartesian product of a closed oriented surface
of positive genus and the circle. As a corollary, we obtain a new proof of a
theorem of Dimca and Suciu by taking N to be the trivial group,