Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
526 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 526 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. #20285445 | C2 | semidirect |
| 2. #20283625 | C2 | semidirect |
| 3. #20276932 | C2 | semidirect |
| 4. #20276930 | C2 | semidirect |
| 5. #20276889 | C2 | semidirect |
| 6. #20276786 | C2 | semidirect |
| 8. #20276610 | C2 | semidirect |
| 9. #20276607 | C2 | semidirect |
| 10. #20276524 | C2 | semidirect |
| 11. C53×#2191 | C2 | semidirect |
| 15. #16811023 | C22 | semidirect |
| 16. #16811008 | C22 | semidirect |
| 24. #16810734 | C22 | semidirect |
| 25. #16810730 | C22 | semidirect |
| 30. #16810446 | C22 | semidirect |
| 31. #16810445 | C22 | semidirect |
| 32. #16810443 | C22 | semidirect |
| 33. #16810439 | C22 | semidirect |
| 34. #16810437 | C22 | semidirect |
| 37. #16810400 | C22 | semidirect |
| 200. #2191 | D53 | semidirect |
| 241. C53 | #33690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285445 | 2 |
| #20283625 | 2 |
| #20276932 | 2 |
| #20276930 | 2 |
| #20276889 | 2 |
| #20276786 | 2 |
| #20276661 | 2 |
| #20276610 | 2 |
| #20276607 | 2 |
| #20276524 | 2 |
| C53×#2191 | 2 |
| #33690 | 53 |