  Compact groups (CGs) of galaxies are extreme environments for morphological
transformations and the cessation of star formation. Our objective is to
understand the dynamics of CGs and how their surrounding environment impacts
galaxy properties. We selected a sample of 340 CGs in the Stripe 82 region,
totaling 1083 galaxies, and a control sample of 2281 field galaxies. We find
that at least 27\% of our sample of CGs are part of major structures, i.e.
non-isolated CGs. We find a bimodality in the effective radius ($R_e$)-S\'ersic
index ($n$) plane for all transition galaxies (those with $(u-r) > 2.3$ and
$n<2.5$) in CGs. Additionally, transition galaxies in isolated CGs populate
more densely the $R_e-n$ plane for $n < 1.75$. In contrast, transition galaxies
in non-isolated CGs have smoothly increasing $n$ values, suggesting these
galaxies have already suffered morphological transformation, and primarily
contribute to the distribution of more compact galaxies in the $R_e-n$ plane
for all transition galaxies in CGs. We also find significant differences in the
specific star-formation rate (sSFR) distribution between the late-type galaxies
(LTGs) ($(u-r)<2.3$ and $n< 2.5$) in non-isolated CGs and the same type of
galaxies in the control sample, suggesting that the evolution of LTGs differs
in non-isolated CGs. Early-type galaxies ($(u-r)>2.3$ and $n>2.5$) and
transition galaxies in non-isolated CGs have lower sSFR values and a higher
fraction of quenched galaxies, compared to those in isolated CGs. Based on our
results, we propose an evolutionary scenario where the major structures in
which the CGs are embedded accelerate the morphological transformations of
their members. Our findings highlight the importance of considering the larger
structures in which CGs may be located, when analysing the properties of their
galaxy, as this can significantly affect the evolution of CGs and their
galaxies.
