"Genre" is originally a French word meaning "kind", "sort" or "type"; in grammatical terminology, it refers to the artificial concept of masculine or feminine grammatical gender (the noun "genre" itself belongs to the masculine gender in French, for example).
In the arts, it refers to the traditional divisions of art forms from a single field of activity (e.g. literature, film, music, painting, sculpture, performance) into various kinds according to criteria particular to that form.
In the field of literary endeavour, we often refer to the "poetic genres" and the "prose genress"; poetry might thus be subdivided into epic, lyric and dramatic, while prose might be divided into fiction and non-fiction. Obviously these can be further subdivided ad libitum: thus, dramatic poetry can be divided into comedy, tragedy, melodrama and so forth. This division can continue more or less as far as one likes: "comedy" has its own genres (farce, comedy of manners, burlesque, satire, etc.).
The divisions called "genres" may be made on the basis of formal, thematic or other criteria. The distinction between fiction and non-fiction thus depends on the use of invention; that between prose and poetry on the use of verse; that between comedy and tragedy on selection and treatment of a protagonist and situation that are noble or vulgar and of a point of view that is sympathetic or not to the protagonist's plight. For this reason, "genre" is such a flexible and mutable term that it has been applied to almost every possible subdivision of artistic endeavour.
Quite clearly, sub-genre might well be more appropriate than "genre" in many, perhaps most cases.