Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
512 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 135 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. #20285374 | C2 | semidirect |
| 2. #20276934 | C2 | semidirect |
| 3. #20276891 | C2 | semidirect |
| 4. #20276796 | C2 | semidirect |
| 6. #20276606 | C2 | semidirect |
| 7. #20276531 | C2 | semidirect |
| 11. #16811025 | C22 | semidirect |
| 12. #16811003 | C22 | semidirect |
| 16. #16810731 | C22 | semidirect |
| 18. #16810447 | C22 | semidirect |
| 19. #16810444 | C22 | semidirect |
| 20. #16810438 | C22 | semidirect |
| 23. #16810401 | C22 | semidirect |
| 193. C53 | #33693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285374 | 2 |
| #20276934 | 2 |
| #20276891 | 2 |
| #20276796 | 2 |
| #20276666 | 2 |
| #20276606 | 2 |
| #20276531 | 2 |
| C53×#2955 | 2 |
| #33693 | 53 |