Polar species are most stable when surrounded by a polar solvent, whilst non-polar species are most stable surrounded by a non-polar solvent. Therefore the structures formed by these molecules will only be stable when the above conditions are fulfilled.
In water we find that the liquid crystals align to form spherical structures called miscelles:
The polar heads are kept in contact with the polar water, whilst shielding the non-polar tails. Similarly, when the liquid crystal is mixed with hexane (a non-polar molecule) we get the following miscelle structure:
Which can be thought of as an inverse of the first, now with the non-polar tails in contact with the non-polar solvent and the polar heads shielded away.
Note that these two structures are only the most basic that will form – varying factors such as concentration of the solute, temperature of the mixture and even the relative polar strength of the head region can result in more complex structures.