The term subdivision refers to a partition of an Indian state below the level of a district but above the level of a subdistrict ('taluk', 'tehsil', 'community development block', 'mandal', or 'circle' depending on the state). In other words, a district may have multiple subdivisions, and one of those subdivisions may contain multiple subdistricts and municipalities.
A subregion or sub-region is a designation for a country subdivision in some countries.
Designations for types of administrative territorial entities
1 Used by ten or more countries or having derived terms. Historical derivations in italics.