Capitalization of official divisions of an organization

Some organizations, like sects, divide themselves into parts—usually, there are two two parts, and those parts are called "outer sect" and "inner sect". These aren’t simply an euphemistic term, like "inner city", but an actual, official division done by the organization itself. This division is both physical and hierarchical. The outer sect is physically separated from the inner sect (they correspond to specific physical areas), and "inner-sect member" and "outer-sect member" are official positions, with the former being hierarchically higher than the latter. In this case, are "outer sect" and "inner sect" actually supposed to be written as "Outer Sect" and "Inner Sect"? And, if that’s the case, would it mean that the correct way to refer to their members is actually "Inner-Sect member" and "Outer-Sect member"?

I believe that, in some companies, divisions such as the "Sales Division" are capitalized, so would "outer sect" and "inner sect" fall under the same category?