We have used the ROSAT PSPC to search for diffuse, extended X-ray emis
sion in a sample of 14 galaxy groups. A diffuse component was found in
four cases. Combining our new analysis with published X-ray observati
ons, we found that a total of 48 galaxy groups of varying size and vel
ocity dispersion have analyzed ROSAT X-ray data. Diffuse, approximate
to 1.0 keV X-ray gas is seen in 25 of the 48 groups analyzed, but the
true incidence of such an intragroup medium is probably lower, since t
his sample includes X-ray-discovered groups. X-ray luminosity does not
correlate well with the optical richness, blue luminosity, or velocit
y dispersion of the group. In contrast, there is a strong correlation
with the percentage of early-type (E and S0) galaxies. All of the grou
ps with an extended intragroup medium have high percentages of early-t
ype galaxies, and over half of these systems appear to contain no spir
als at all. Furthermore, all the X-ray-detected systems contain at lea
st one elliptical with a blue luminosity of L(B) similar to 5 x 10(10)
L(.) or greater. We discuss several possible explanations for the cor
relation between spiral fraction and the presence of diffuse hot gas,
including the idea that the spiral-rich groups represent superposition
s of galaxies, that they contain a relatively cool intragroup medium,
or that the formation and evolution of spiral-rich groups are fundamen
tally different from those of elliptical-rich groups. We also use the
X-ray observations to estimate the total masses of these systems. Ther
e is a large range in the derived gas masses, but in general the mass
in the X-ray-emitting gas is comparable to or less than the mass in th
e galaxies. Despite the large range in gas mass, there is a very narro
w range in total group mass, with most of the groups having a mass of
similar to 2 x 10(13) M(.) out to the radius for which X-ray emission
is detected by ROSAT. The ratio of observed luminous mass (i.e., galax
ies + hot gas) to total inferred mass in poor groups is rather low (ap
proximate to 5%-30%), implying that these systems are dominated by dar
k matter.