In considering crystal symmetries, crystallographers tend to think in terms of particular configurations. In using nonlinear continuum theory to analyze such things as phase transitions and twinning, one needs to consider a variety of configurations having different symmetries. Correlating these leads to some unanswered questions in crystallography. This article deals with one that relates to continuum descriptions of crystal multilattices. Briefly, one can encounter ambiguities in describing symmetries of configurations for a subset of the configurations of interest. Primarily, the aim here is to characterize such subsets.