We have measured 125 redshifts in 31 groups of galaxies observed with Einstein, and have compiled an additional 543 redshifts from the literature. There is a correlation between galaxy surface density and group velocity dispersion, with mu alpha sigma(1.6+/-0.6), but the scatter about this relation is large. We examine the relationship between the group x-ray luminosity in the 0.3-3.5 keV band and the measured velocity dispersion. Richer groups follow the same relation as rich clusters [cf. Quintana and Melnick, AJ, 87, 972 (1982)] with L(x) alpha sigma(4.0+/-0.6), but the relation flattens for lower luminosity systems which have velocity dispersions below 300 km s(-1). We suggest that the L(x)-sigma relation arises from a combination of extended cluster emission and emission associated with individual galaxies. The x-ray emission for the richer groups is dominated by emission from the intragroup medium, as for the richer clusters; emission from the poorer clusters is dominated by less extended emission associated with the individual group galaxies.