Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
512 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21456473 | C2 | semidirect |
| 3. #21448039 | C2 | semidirect |
| 4. #21448036 | C2 | semidirect |
| 5. #21447993 | C2 | semidirect |
| 6. #21447898 | C2 | semidirect |
| 8. #21447711 | C2 | semidirect |
| 9. #21447707 | C2 | semidirect |
| 10. #21447632 | C2 | semidirect |
| 15. #16840162 | C22 | semidirect |
| 16. #16840140 | C22 | semidirect |
| 24. #16839869 | C22 | semidirect |
| 25. #16839868 | C22 | semidirect |
| 30. #16839585 | C22 | semidirect |
| 31. #16839584 | C22 | semidirect |
| 32. #16839582 | C22 | semidirect |
| 33. #16839579 | C22 | semidirect |
| 34. #16839578 | C22 | semidirect |
| 37. #16839539 | C22 | semidirect |
| 240. C61 | #33693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456473 | 2 |
| #21454722 | 2 |
| #21448039 | 2 |
| #21448036 | 2 |
| #21447993 | 2 |
| #21447898 | 2 |
| #21447770 | 2 |
| #21447711 | 2 |
| #21447707 | 2 |
| #21447632 | 2 |
| C61×#2191 | 2 |
| #33693 | 61 |