I'm looking for criteria to know if a (lie) group is unimodular, the thing is that I only know one non unimodualr group that arrises naturaly, the affine group ax+b, and their direct generalizations. I have the intuition that the Galilean and Lorentz group are unimodular but I haven done the calculation yet, I would be happy to see more explamples especially in dimension 3 and of type I. I'm tempted to say that unimodular groups are simply connected and or soluble but I need more examples to work with.
Edit: the poincare group is semisimple, hence unimodular.