  In this paper, we investigate behaviors of Maximal Dimension, a group
invariant involving certain configuration of maximal subgroups, which we denote
by MaxDim. We prove that in some special cases, MaxDim(G\times H) = MaxDim(G) +
MaxDim(H). We also prove a conjecture stated by Ellie Thieu which shows that
groups with m < MaxDim can be constructed from groups with m < i.
