Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
536 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20283619 | C2 | semidirect |
| 2. #20276927 | C2 | semidirect |
| 3. #20276888 | C2 | semidirect |
| 4. #20276788 | C2 | semidirect |
| 5. #20276660 | C2 | semidirect |
| 6. #20276611 | C2 | semidirect |
| 7. #20276531 | C2 | semidirect |
| 8. C53×#3176 | C2 | semidirect |
| 18. #16810445 | C22 | semidirect |
| 19. #16810444 | C22 | semidirect |
| 20. #16810436 | C22 | semidirect |
| 23. #16810401 | C22 | semidirect |
| 25. C53×#499 | C22 | semidirect |
| 26. C53×#493 | C22 | semidirect |
| 30. C53×#442 | C22 | semidirect |
| 162. #3176 | D53 | semidirect |
| 179. #499 | C2×D53 | semidirect |
| 180. #493 | C2×D53 | semidirect |
| 188. #442 | C2×D53 | semidirect |
| 199. C53 | #33692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283619 | 2 |
| #20276927 | 2 |
| #20276888 | 2 |
| #20276788 | 2 |
| #20276660 | 2 |
| #20276611 | 2 |
| #20276531 | 2 |
| C53×#3176 | 2 |
| #33692 | 53 |