The nature and origin of the glass transition is one of the great unsolved problems of condensed-matter science. With the rapid increase of viscosity upon cooling the liquid near the glass-transition temperature, a range of dynamical motifs are observed, revealing the sheer complexity of interactions between the amorphous units. Yet, the causal link between those motifs and the solidification process remains unclear. Here, we apply a novel approach for exploring nontrivial interactions between structural units in D-sorbitol, a canonical example of a hydrogen-bonded organic glass, by introducing a dihedralrearrangement-indicator analysis to shed light on relaxation processes and dynamical heterogeneity, which are known for their association with the stability of a glass. We find that both alpha- and beta-relaxation processes are governed by cooperative and heterogeneous changes in hydrogen-bond dynamics that can be described by spatial and dihedral-angle-rearrangement indicators. The methodology and findings are of general applicability to other glass-forming systems.