Hi @apaglione,
In Canvas, a "group" is like a "team." Canvas Groups are set up for collaborative assignments and discussions. Since Quizzes can only be done individually, you cannot set up a "Group Quiz."
If, however, you only want some of your students to take the Quiz, you can enter the individual student names into the Assignment box (where you enter the dates.) Another option is to create a "Section" (or "Sections"). Then you can assign students to a "Section" and give them a different Quiz (or Assignment) than the rest of your class. In this case, the students in that Section will all take the Quiz individually.
Please let us know if you have additional questions.