Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
512 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 121 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. #20285369 | C2 | semidirect |
| 3. #20276934 | C2 | semidirect |
| 4. #20276890 | C2 | semidirect |
| 5. #20276795 | C2 | semidirect |
| 8. #20276609 | C2 | semidirect |
| 9. #20276605 | C2 | semidirect |
| 10. #20276528 | C2 | semidirect |
| 11. C53×#2239 | C2 | semidirect |
| 17. #16811023 | C22 | semidirect |
| 18. #16811001 | C22 | semidirect |
| 26. #16810730 | C22 | semidirect |
| 27. #16810729 | C22 | semidirect |
| 31. #16810447 | C22 | semidirect |
| 32. #16810443 | C22 | semidirect |
| 33. #16810438 | C22 | semidirect |
| 37. #16810400 | C22 | semidirect |
| 40. C53×#365 | C22 | semidirect |
| 41. C53×#362 | C22 | semidirect |
| 197. #2239 | D53 | semidirect |
| 231. #365 | C2×D53 | semidirect |
| 234. #362 | C2×D53 | semidirect |
| 240. C53 | #33693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285369 | 2 |
| #20283617 | 2 |
| #20276934 | 2 |
| #20276890 | 2 |
| #20276795 | 2 |
| #20276668 | 2 |
| #20276665 | 2 |
| #20276609 | 2 |
| #20276605 | 2 |
| #20276528 | 2 |
| C53×#2239 | 2 |
| #33693 | 53 |