Symmetry numbers are essential in thermochemistry and chemical kinetics, but their reliable assignment remains difficult in automated workflows, especially for stereochemical, fluxional, cyclic, and transition-state structures. We present a stereochemistryaware automorphism (SAA) approach for computing symmetry numbers using the StereoMolGraph (SMG) framework. In this representation, local stereodescriptors encode rigid local geometries directly in the molecular graph, so the symmetry number is obtained as the order of the automorphism group that preserves both connectivity and encoded stereochemistry. This avoids the need for a post hoc “label stereocenter” correction and provides a direct graph-theoretical analogue of permutation-based symmetry number definitions. Model dependence is handled explicitly by choosing which molecular features are treated as fixed or fluxional, enabling consistent treatment of rigidity, free rotation, umbrella inversion, and pseudorotation assumptions. Beyond overall molecular and transition-state symmetry numbers, the same framework yields external and internal symmetry numbers for hindered-rotor treatments. Benchmark calculations reproduce the expected symmetry numbers for all supported benchmark molecules and resolve cases where existing rule-based or corrected-connectivity approaches fail. The SAA approach is highly robust, making it suitable for automated thermochemical and kinetic modeling of molecules and reactions.