Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
686 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 159 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. #499×D53 | C2 | semidirect |
| 3. #20276958 | C2 | semidirect |
| 4. #20276957 | C2 | semidirect |
| 5. #20276956 | C2 | semidirect |
| 6. #20276955 | C2 | semidirect |
| 7. #357×D53 | C2 | semidirect |
| 8. #346×D53 | C2 | semidirect |
| 9. C53×#2244 | C2 | semidirect |
| 15. #16811025 | C22 | semidirect |
| 16. #16811024 | C22 | semidirect |
| 26. #16810425 | C22 | semidirect |
| 27. #16810424 | C22 | semidirect |
| 28. #16810423 | C22 | semidirect |
| 29. #16810399 | C22 | semidirect |
| 30. #16810398 | C22 | semidirect |
| 31. C53×#499 | C22 | semidirect |
| 33. C53×#357 | C22 | semidirect |
| 34. C53×#346 | C22 | semidirect |
| 157. #2244 | D53 | direct (N × H) |
| 164. D53 | #2244 | direct (N × H) |
| 174. #499 | C2×D53 | semidirect |
| 186. #357 | C2×D53 | semidirect |
| 189. #346 | C2×D53 | semidirect |
| 190. C53 | C2×#2244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #499×D53 | 2 |
| #493×D53 | 2 |
| #20276958 | 2 |
| #20276957 | 2 |
| #20276956 | 2 |
| #20276955 | 2 |
| #357×D53 | 2 |
| #346×D53 | 2 |
| C53×#2244 | 2 |
| C2×#2244 | 53 |