We demonstrate that Longuet-Higgins' molecular symmetry (MS) group for describing non-rigid molecules allows deduction of the transition state for an intramolecular rearrangement and that the level of symmetry of the transition state is governed by very simple rules. Key pieces of information are the order of the MS group and the number of distinctly labelled forms represented by it. We also show that the local symmetry at stationary points on the potential energy surface is important and introduce natural definitions of narcissistic reactions and pathways using the laboratory-fixed inversion operation, giving examples of each. Inspection of normal modes is used to depict motion across the potential energy surface between a minimum-energy structure and a transition state. This analysis is applied to acetylene trimer, a recently observed van der Waals cluster. We elucidate the relationships between the stationary points identified by our earlierab initiowork. There are two transition state structures that together allow full interconversion between the 16 distinctly labelled forms of the global minimum.