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Superficially it seems like people who are seated closer to the front would be in earlier groups but that often doesn't seem to be the case. Like the other day I was in seat 7A and in Group 3 on a 737.

So how are boarding groups determined? Is it random? Maybe it is partially based on seat number but other factors are taken into consideration?

Every airline will use different boarding procedures, taking into account everything from priority passengers (business class, frequent flyers), what people have paid for, through to the quickest way to board the plane.

As a result, no two airlines will generally have the same process. To give two examples, American Airlines (which it looks like you were on) boards First Class, Business class, high-level frequent flyers, lower-level frequent flyers, then Groups 1 through 4.

Group 1 is people that have paid for early board, credit card holders, etc
Group 2 is people that use Online check-in, or are connecting from another airline
Group 3 is people that used a self-serve Kiosk to check-in.
Group 4 is people that used an agent to check-in.

By contrast, United Airlines boards using groups 1-5, which are :

Group 1 is Business/First class passengers, as well as high-level frequent flyers.
Group 2 is lower less frequent flyers, people that have paid for early boarding, and people with United-branded credit cards that allow early boarding.
Group 3 is all remaining passengers that are in window seats.
Group 4 is all remaining passengers in middle seats.
Group 5 is everyone else (ie, aisle seats)

(Both also have things like people with disabilities/wheelchairs/etc, military, and so on that I've ignored)

Looking at https://www.seatguru.com/articles/boarding_procedures.php , it seems that American Airlines (which you tagged) is mainly boarding back-to-front:

American, as well as most domestic and international carriers, uses the standard "Rear-to-Front" boarding. In the case of American, Elites, followed by ffirst and business class passengers, as well as uniformed members of the US military, board first, followed by flyers holding elite status with American Airlines, US Airways and oneworld alliance airlines.. Group 1 boarding -- which can be purchased or obtained with certain fares – boards next. Finally, Then, seats in the back of the plane are boarded followed by the middle section and then the front area.

If you're asking about American Airlines (AA) specifically, and not general US based airlines, it goes pretty much like:

1. Special Assistence


2. Class of Service - First, Business


3. Uniformed Military


4. AAdvantage Status


5. Fare Class - Full fare vs. discount


6. Optional Services - PriorityAAcess/Main Cabin Extra


7. Chick-in time*


8. Algorithm to distribute everyone else.

*Disclaimer: I don't know if this is still the case.