  We consider integrable Hamiltonian systems in three degrees of freedom near
an elliptic equilibrium in 1:1:-2 resonance. The integrability originates from
averaging along the periodic motion of the quadratic part and an imposed
rotational symmetry about the vertical axis. Introducing a detuning parameter
we find a rich bifurcation diagram, containing three parabolas of Hamiltonian
Hopf bifurcations that join at the origin. We describe the monodromy of the
resulting ramified 3-torus bundle as variation of the detuning parameter lets
the system pass through 1:1:-2 resonance.
