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### Symmetry and Order under a Continous Change

As one can read from the Formation Process part and the Classification part, it's important to get the order parameter space by look at the ordered phase and the leftover symmetries of the system. As the energy scale of the system change, the system goes through many transitions of phases with distinct symmetrical properties. Consider the above picture showing 4 different phases of liquid crystal. Suppose the system starts in a disordered phase at a high temperature and gradually decrease temperature, and as the energy scale goes down the ordered phase becomes less symmetric. Can you identify the symmetry group of these phase and the sequence of phase transitions?