We combine video recording and laser range tracking to analyse the geometrical structure of groups of walking pedestrians socially interacting. By recording their relative position and observing their social interaction for a large enough time span we can analyse the stability and universality of their spatial structure. We find that while 2-pedestrian and 3-pedestrian groups have a relatively ``time stable'' and ``universal'' geometrical structure (an abreast formation for pairs, and a ``V'' formation for triads, with the central pedestrian walking slightly behind), no such structure emerges for larger groups. Nevertheless, these larger groups result to be composed of time stable two or three people sub-groups with the same ``universal'' geometrical structure of isolated pairs and triads.