The semiclassical methods of periodic-orbit quantization and equilibrium-point quantization are compared from a theoretical point of view and in the application to the transition-state resonances of a collinear dissociation model for the HgI2 molecule. The classical dynamics, semiclassical quantization, and quantum resonance states of this system are discussed in detail. The system features a transition from classically regular to chaotic dynamics, the transition being initiated by a pitchfork-type bifurcation which may be characterized in terms of a normal form. In the regular regime, the results of equilibrium-point quantization and periodic-orbit quantization are shown to be in good agreement. We discuss the results of periodic-orbit quantization for the chaotic regime, which we recently reported (Burghardt, I.; Gaspard, P. J. Chem. Phys. 1994, 100, 6395.), under the aspect of the symbolic dynamics which provides a classification scheme far the periodic orbits. The symbolic dynamics is shown to be attached to the phase-space structure of a Smale horseshoe, for which we provide numerical evidence in the HgI2 system. We compare with an alternative symbolic-dynamics scheme, which is based on the symmetry of the system and allows for the reduction of the dynamics to a fundamental domain. We thus obtain a comprehensive picture of the classical and quantum properties of the dissociation process.