Sub-monolayer amounts of trioxatriangulenium (TOTA) molecules functionalized with biphenyl on Ag(111) were investigated with scanning tunnelling microscopy. The molecule is comprised of a rod-shaped axial ligand and a triangular platform that tends to form hydrogen bonds in arrays. Two superstructures are observed, a hexagonal tiling and a phase of molecular double rows. While the former structure matches previous observations from other functionalized TOTA molecules the latter one was unexpected. Aided by density functional theory results, we analyse the observed intramolecular contrast and present a model of the new phase. We discuss possible interaction mechanisms underlying the molecular pattern.