Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
520 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 520 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. #20285458 | C2 | semidirect |
| 3. #20276933 | C2 | semidirect |
| 4. #20276887 | C2 | semidirect |
| 5. #20276886 | C2 | semidirect |
| 6. #20276793 | C2 | semidirect |
| 8. #20276609 | C2 | semidirect |
| 9. #20276607 | C2 | semidirect |
| 10. #20276526 | C2 | semidirect |
| 11. C53×#2214 | C2 | semidirect |
| 16. #16811021 | C22 | semidirect |
| 26. #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 |
| 214. #2214 | D53 | semidirect |
| 230. #494 | C2×D53 | semidirect |
| 248. #364 | C2×D53 | semidirect |
| 250. #362 | C2×D53 | semidirect |
| 255. C53 | #33689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285458 | 2 |
| #20283620 | 2 |
| #20276933 | 2 |
| #20276887 | 2 |
| #20276886 | 2 |
| #20276793 | 2 |
| #20276664 | 2 |
| #20276609 | 2 |
| #20276607 | 2 |
| #20276526 | 2 |
| C53×#2214 | 2 |
| #33689 | 53 |