Recent experimental studies have shown that T-shaped bolaamphiphiles (TBA) with a swallow-tail lateral chain display several thermotropic liquid crystalline phases depending on the size of the lateral chain and temperature. In this work, we use molecular simulations of a simple coarse-grained model to map out the phase behavior of this type of molecules. This model is based on the premise that the crucial details of the fluid structure stem from close range repulsions and the strong directional force typical of hydrogen bonds. Our simulations confirm that TBAs exhibit a rich phase behavior upon increasing the length of their lateral chain. The simulations successfully detect the double gyroid phase and the axial-bundle columnar phase, whose structures are similar to those found in experiment. In addition, simulations predict two cocontinuous phases with 3D-periodicity (the “single” diamond and the “single” plumber’s nightmare phase) yet to be reported in experimental studies. The structure factor and several 2D order parameters are used to identify and characterize these liquid crystal phases. D1.avi and P1.avi are provided as supplementary materials to confirm that these ordered phases have some fluidity consistent with a liquid crystal character.