Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
512 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 512 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 |
|---|---|---|
| 2. #20276932 | C2 | semidirect |
| 3. #20276888 | C2 | semidirect |
| 4. #20276793 | C2 | semidirect |
| 6. #20276604 | C2 | semidirect |
| 7. #20276531 | C2 | semidirect |
| 8. C53×#3177 | C2 | semidirect |
| 18. #16810445 | C22 | semidirect |
| 19. #16810444 | C22 | semidirect |
| 20. #16810439 | C22 | semidirect |
| 23. #16810401 | C22 | semidirect |
| 25. C53×#499 | C22 | semidirect |
| 26. C53×#494 | C22 | semidirect |
| 30. C53×#441 | C22 | semidirect |
| 157. #3177 | D53 | semidirect |
| 173. #499 | C2×D53 | semidirect |
| 174. #494 | C2×D53 | semidirect |
| 182. #441 | C2×D53 | semidirect |
| 193. C53 | #33693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283619 | 2 |
| #20276932 | 2 |
| #20276888 | 2 |
| #20276793 | 2 |
| #20276665 | 2 |
| #20276604 | 2 |
| #20276531 | 2 |
| C53×#3177 | 2 |
| #33693 | 53 |