Hello! Unfortunately, I could not solve the problem because none of the above mentioned options appear in my version of Moodle. But I found out that the students cannot see the groups anyway. I switched roles to see the course as a student and also I checked with my students and they told me that they cannot see the groups. I believe it all depends on the your Moodle settings and whether you can change the settings or not.
If it helps, you can see the version of Moodle in use if you click at the bottom of the page on Moodle Docs. At the top of that page it will show the version.