Let Gamma be a non-Euclidean crystallographic group. Gamma is said to be non-maximal if there exists a non-Euclidean crystallographic group Gamma' such that Gamma <= Gamma' and the dimension of the Teichmuller space of Gamma equals the dimension of the Teichmuller space of V. The full list Of such pairs of groups is computed in the case when Gamma is non-normal in Gamma'. The corresponding problem for Fuchsian groups was solved by Singerman.