Nonsymmetrical organic molecules adsorbed on solid surfaces may assemble into random networks, thereby providing model systems for organic glasses that can be directly observed by scanning tunneling microscopy (STM). We investigated the structure of a disordered cytosine network on a gold(111) surface created by thermal quenching, to temperatures below 150 K, of the two-dimensional fluid present on the surface at room temperature. Comparison of STM images to density functional theory calculations allowed us to identify three elementary structural motifs (zigzag filaments and five- and six-membered rings) that underlie the whole supramolecular random network. The identification of elementary structural motifs may provide a new framework for understanding medium-range order in amorphous and glassy systems.