The Lyapunov exponents are calculated for the trajectories in the quantum phase space of the eigenstates of the highly excited C-H bend motion of acetylene. For a state, if there is only one Lyapunov exponent, the corresponding dynamics is ergodic. Quite often, there are the cases that the Lyapunov exponents for a state span a wide spectrum. This means that the motion cannot be ergodic. Stable and unstable periodic trajectories and the transition between the regions in the quantum phase space with various degrees of irregularity are also identified, showing that the dynamical structure is quite complex.