We have derived the X-ray luminosities of a sample of galaxies in groups, making careful allowance for contaminating intragroup emission. The L-X : L-B and L-X : L-FIR relations of spiral galaxies in groups appear to be indistinguishable from those in other environments, however the elliptical galaxies fall into two distinct classes. The first class is central-dominant group galaxies, which are very X-ray luminous and may be the focus of group cooling flows. All other early-type galaxies in groups belong to the second class, which populates an almost constant band of L-X/L-B over the range 9.8 <log L-B <11.3. The X-ray emission from these galaxies can be explained by a superposition of discrete galactic X-ray sources together with a contribution from hot gas lost by stars, which varies a great deal from galaxy to galaxy. In the region where the optical luminosity of the non-central group galaxies overlaps with the dominant galaxies, the dominant galaxies are over an order of magnitude more luminous in X-rays. We also compared these group galaxies with a sample of isolated early-type galaxies, and used previously published work to derive L-X : L-B relations as a function of environment. The non-dominant group galaxies have mean L-X/L-B ratios very similar to those of isolated galaxies, and we see no significant correlation between L-X/L-B and environment. We suggest that previous findings of a steep L-X : L-B relation for early-type galaxies result largely from the inclusion of group-dominant galaxies in samples.