Hi.
You need to check the flame sensor, hi-limit, cut-off thermal fuse.
Most likely it's the flame sensor. You can try to jump it and if the ignitor start glowing - replace the flame sensor.
Part number: 338906
Here are the breakdown diagrams and
Replacement parts for Maytag AGD4475TQ0 29" GAS DRYER | AppliancePartsPros.com
Post the results.
Simon.