  We present quantitative morphology measurements of a sample of optically
selected group galaxies at 0.3 < z < 0.55 using the Hubble Space Telescope
(HST) Advanced Camera for Surveys (ACS) and the GIM2D surface
brightness--fitting software package. The group sample is derived from the
Canadian Network for Observational Cosmology Field Redshift survey (CNOC2) and
follow-up Magellan spectroscopy. We compare these measurements to a similarly
selected group sample from the Millennium Galaxy Catalogue (MGC) at 0.05 < z <
0.12. We find that, at both epochs, the group and field fractional bulge
luminosity (B/T) distributions differ significantly, with the dominant
difference being a deficit of disk--dominated (B/T < 0.2) galaxies in the group
samples. At fixed luminosity, z=0.4 groups have ~ 5.5 +/- 2 % fewer
disk--dominated galaxies than the field, while by z=0.1 this difference has
increased to ~ 19 +/- 6 %. Despite the morphological evolution we see no
evidence that the group environment is actively perturbing or otherwise
affecting the entire existing disk population. At both redshifts, the disks of
group galaxies have similar scaling relations and show similar median
asymmetries as the disks of field galaxies. We do find evidence that the
fraction of highly asymmetric, bulge--dominated galaxies is 6 +/- 3 % higher in
groups than in the field, suggesting there may be enhanced merging in group
environments. We replicate our group samples at z=0.4 and z=0 using the
semi-analytic galaxy catalogues of Bower et al (2006). This model accurately
reproduces the B/T distributions of the group and field at z=0.1. However, the
model does not reproduce our finding that the deficit of disks in groups has
increased significantly since z=0.4.
