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. #20285375 | C2 | semidirect |
| 3. #20276936 | C2 | semidirect |
| 4. #20276888 | C2 | semidirect |
| 5. #20276797 | C2 | semidirect |
| 6. #20276796 | C2 | semidirect |
| 8. #20276605 | C2 | semidirect |
| 9. #20276603 | C2 | semidirect |
| 10. #20276530 | C2 | semidirect |
| 11. C53×#2231 | C2 | semidirect |
| 17. #16811003 | C22 | semidirect |
| 26. #16810729 | C22 | semidirect |
| 31. #16810445 | C22 | semidirect |
| 32. #16810444 | C22 | semidirect |
| 33. #16810440 | C22 | semidirect |
| 34. #16810438 | C22 | semidirect |
| 37. #16810400 | C22 | semidirect |
| 38. C53×#499 | C22 | semidirect |
| 40. C53×#365 | C22 | semidirect |
| 41. C53×#364 | C22 | semidirect |
| 206. #2231 | D53 | semidirect |
| 223. #499 | C2×D53 | semidirect |
| 240. #365 | C2×D53 | semidirect |
| 242. #364 | 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 |
|---|---|
| #20285375 | 2 |
| #20283613 | 2 |
| #20276936 | 2 |
| #20276888 | 2 |
| #20276797 | 2 |
| #20276796 | 2 |
| #20276667 | 2 |
| #20276605 | 2 |
| #20276603 | 2 |
| #20276530 | 2 |
| C53×#2231 | 2 |
| #33693 | 53 |