1. To contain several smaller parts, sections, or subcategories. There is one massive parent company running the whole operation that then subdivides into smaller subsidiaries responsible for various different kinds of businesses. Most people know what a noun is, but not everyone knows that the term subdivides into a bunch of different types of nouns, such as common nouns, proper nouns, concrete nouns, and so on.

2. To divide something down into smaller parts, sections, or subcategories. In this usage, a noun or pronoun is used between "subdivide" and "into." The easiest way to calculate the area of these complicated shapes is to subdivide them into smaller, simpler shapes and add up the totals of all their areas. I think we should subdivide the project into sections that the different teams can work on separately.