KöMaL 2022 B5278

In Noname School of Nowhere, the graduating class consists of four groups, each specializing in a different subject: math, physics, chem and bio. On day, they are all sitting around a large round table in the school cafeteria: everyone has someone sitting directly opposite them, and everyone has neighbours sitting right next to them on either side. However a student is selected, it is observed that this student, the two neighbours, and the one sitting straight across the table all belong to different groups. How many students may there be in the graduating class if there are less than $20$ of them?