We present a low-temperature scanning tunneling microscopy study on the self-assembly of extended polycyclic aromatic hydrocarbons with different symmetries on the Cu(111) surface. All molecules show a commensurate monolayer structure, with significant structural differences with respect to the unit cell of the molecular lattice and the orientational ordering. We find that the molecular lattice and the molecular orientation are largely dominated by molecule-substrate interactions, whereas molecule-molecule interactions determine the molecular packing density via steric repulsion. Moreover, we show that the structure of the monolayer is transferred to the second layer via molecule-molecule interaction.