  Group synchronization arises when two or more synchronization patterns
coexist in a network formed of oscillators of different types, with the systems
in each group synchronizing on the same time-evolution, but systems in
different groups synchronizing on distinct time-evolutions. Group
synchronization has been observed and characterized when the systems in each
group are identical and the couplings between the systems satisfy specific
conditions. By relaxing these constraints and allowing them to be satisfied in
an approximate rather than exact way, we observe that stable group
synchronization may still occur in the presence of small deviations of the
parameters of the individual systems and of the couplings from their nominal
values. We analyze this case and provide necessary and sufficient conditions
for stability through a master stability function approach, {which also allows
us to quantify the synchronization error}. We also investigate the stability of
group synchronization in the presence of intra group connections and for this
case, extend some of the existing results in the literature. Our analysis
points out a broader class of matrices describing intra group connections for
which the stability problem can be reduced in a low-dimensional form.
