Dissipative particle dynamics (DPD) simulations are used to model the aqueous self-assembly of three variants of the non-ionic triphenylene-based chromonic mesogen, TP6EO2M. In the variants studied, one to three of the six methoxy poly(ethylene glycol) chains of TP6EO2M are replaced by short hydrophobic-lipophobic chains, causing a remarkable change in the structure of the mesophases formed. In the 100 wt% limit, corresponding to pure thermotropic phases, complex columnar phases arise, in which the underlying hexagonal packing is supplemented by additional order resulting from microphase separation of hydrophobic-lipophobic regions. With addition of water an array of novel chromonic phases are seen. In these phases supramolecular aggregates form in which hydrophobic-lipophobic chains are excluded from water by the joining together of single molecule chromonic stacks into dimers or trimers. These aggregates form chromonic N and M phases and, in the case of a "Janus mesogen" (with three hydrophobic-lipophobic chains on one side of the molecule), form a novel smectic chromonic phase. Spontaneous symmetry breaking is seen in columns composed of trimer stacks with defects. Here achiral molecular aggregates develop a spontaneous twist, inducing the formation of either left-handed or right-handed chiral aggregates. On the long time-scales accessible to DPD simulations, chiral aggregates are seen to be dynamic structures in which chirality inversion can take place over long periods of time.