Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
520 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 520 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. #20285455 | C2 | semidirect |
| 3. #20276935 | C2 | semidirect |
| 4. #20276932 | C2 | semidirect |
| 5. #20276884 | C2 | semidirect |
| 6. #20276794 | C2 | semidirect |
| 8. #20276607 | C2 | semidirect |
| 9. #20276603 | C2 | semidirect |
| 10. #20276524 | C2 | semidirect |
| 15. #16811020 | C22 | semidirect |
| 16. #16811001 | C22 | semidirect |
| 24. #16810730 | C22 | semidirect |
| 25. #16810729 | C22 | semidirect |
| 30. #16810446 | C22 | semidirect |
| 31. #16810445 | C22 | semidirect |
| 32. #16810443 | C22 | semidirect |
| 33. #16810440 | C22 | semidirect |
| 34. #16810439 | C22 | semidirect |
| 37. #16810400 | C22 | semidirect |
| 237. C53 | #33689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285455 | 2 |
| #20283625 | 2 |
| #20276935 | 2 |
| #20276932 | 2 |
| #20276884 | 2 |
| #20276794 | 2 |
| #20276666 | 2 |
| #20276607 | 2 |
| #20276603 | 2 |
| #20276524 | 2 |
| C53×#2191 | 2 |
| #33689 | 53 |