To make a group reservation, you must adhere to American Airlines' group travel policy, which includes things like

You can go to the official website and look for the reservation section to reserve a flight for a group of people by American Airlines Group Travel.

Choose the group trip option under "booking" and continue.

Please indicate your preferred location, date, and time. Choose if you are going one way or round trip in addition to that.

Next, indicate the number of passengers and choose the payment method from cash, card, or miles.

Once finished, choose a flight. Make a payment after selecting a flight, and your flight reservations are complete.