  We estimate the distribution of intrinsic shapes of UZC-SSRS2 groups of
galaxies from the distribution of their apparent shapes. We measure the
projected group axial ratio using the moments of their discrete galaxy
distribution. Then using the non-parametric kernel method to estimate the
smooth apparent axial ratio distribution we numerically invert a set of
integral equations to recover the corresponding intrinsic distribution under
the assumption that groups are either oblate or prolate spheroids. We find that
the prolate spheroidal model fits very well the UZC-SSRS2 group distribution
with a true mean axial ratio <\beta>~0.3 and \sigma ~0.15. This shows that
groups of galaxies are significantly more elongated, both on the plane of the
sky and in 3 dimensions, than clusters of galaxies. The poorest groups that we
consider, those with 4 members, are even more elongated than the overall
population with 85% of the groups having \beta < 0.4.
