Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
512 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20285371 | C2 | semidirect |
| 3. #20276933 | C2 | semidirect |
| 4. #20276892 | C2 | semidirect |
| 5. #20276891 | C2 | semidirect |
| 6. #20276793 | C2 | semidirect |
| 8. #20276609 | C2 | semidirect |
| 9. #20276607 | C2 | semidirect |
| 10. #20276530 | C2 | semidirect |
| 11. C53×#2214 | C2 | semidirect |
| 16. #16811025 | C22 | semidirect |
| 25. #16810730 | C22 | semidirect |
| 30. #16810447 | C22 | semidirect |
| 31. #16810446 | C22 | semidirect |
| 32. #16810444 | C22 | semidirect |
| 33. #16810439 | C22 | semidirect |
| 37. #16810400 | C22 | semidirect |
| 39. C53×#494 | C22 | semidirect |
| 41. C53×#364 | C22 | semidirect |
| 42. C53×#362 | C22 | semidirect |
| 208. #2214 | D53 | semidirect |
| 224. #494 | C2×D53 | semidirect |
| 242. #364 | C2×D53 | semidirect |
| 244. #362 | C2×D53 | semidirect |
| 249. C53 | #33693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285371 | 2 |
| #20283613 | 2 |
| #20276933 | 2 |
| #20276892 | 2 |
| #20276891 | 2 |
| #20276793 | 2 |
| #20276664 | 2 |
| #20276609 | 2 |
| #20276607 | 2 |
| #20276530 | 2 |
| C53×#2214 | 2 |
| #33693 | 53 |