a subdivision of a facet, based on inherent categories
Subfacets, like facets, should be defined so that they are mutually exclusive. For example, an "agents" facet might be subdivided into "individuals" and "organisations" subfacets; an "activities" facet might be subdivided into transitive "actions" and intransitive "processes" subfacets.
Some writers use the term "subfacet" as synonymous with array, or with the slightly broader meaning of the whole subtree of concepts grouped under a node label showing a characteristic of division, rather than just the first level array of sibling terms. I suggest that it should not be used with these meanings, as the intuitive meaning is "a subdivision of a facet" and we already have the terms "array" and "subtree" for the other meanings.