The majority of hot subdwarf stars are low-mass core-helium-burning stars. Their atmospheres are generally helium deficient; however, a minority have extremely helium-rich surfaces. An additional fraction have an intermediate surface-helium abundance, occasionally accompanied by peculiar abundances of other elements. We have identified a sample of 88 hot subdwarfs including 38 helium-deficient, 27 intermediate-helium and 23 extreme-helium stars for which radial-velocity and proper-motion measurements, together with distances, allow a calculation of galactic space velocities. We have investigated the kinematics of these three groups to determine whether they belong to similar or different Galactic populations. The majority of helium-deficient subdwarfs in our sample show a kinematic distribution similar to that of thick disc stars. Helium-rich sdBs show a more diverse kinematic distribution. Although the majority are probably disc stars, a minority show a much higher velocity dispersion consistent with membership of a Galactic halo population. Several of the halo subdwarfs are members of the class of ‘heavy-metal’ subdwarfs discovered by Naslim et al.