[GAP Forum] computing maximal transitive subgroups of a transitive group

[Bill Allombert]

Dear GAP forum,

I need to compute the maximal transitive subgroups of a transitive
group (grouped by conjugacy classes).

For example for S4, I should get A4 and two conjugate copies of D4.

I managed to do the computation for all transitive groups of degree
<=13, but for 14 it become quite slow.

Are there good algorithms to solve this problem ?

Thanks in advance for your help!
Bill.