Let's say there's a high school where you can study different subjects and you choose which group you want to go to. For example if you like IT you can choose a group where the number of IT lessons is the biggest. Or if you like the army, you can choose a group where there is quite a lot of classes about the army and the such, etc. Of course apart from these subjects, like IT for instance, the students also learn maths, biology, geography etc.

Is it OK to say: In our school there are IT oriented groups, business oriented groups, agriculture oriented groups, army oriented groups etc.

What's the most natural way to say that?

The word "oriented" is OK to use like that. From what I've seen, it most often occurs with a hyphen.

business-oriented groups

Students: Are you brave enough to let our tutors analyse your pronunciation?
Yes, the "oriented" is fine. A hyphen makes it clearer: IT-oriented, military-oriented, etc.

Another good adjective might be focus: various groups focus on different areas such as IT, military science, and XXX while continuing a core curriculum of basic subjects.
Thanks for the answers guys!