Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
748 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 748 conjugacy classes of subgroups — too many to draw. Only its 163 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. C2×#16811058 | C2 | semidirect |
| 2. C22×D848 | C2 | semidirect |
| 3. #20285202 | C2 | semidirect |
| 4. #20283566 | C2 | semidirect |
| 5. #20276773 | C2 | semidirect |
| 6. #20276749 | C2 | semidirect |
| 7. #20276473 | C2 | semidirect |
| 8. #20276430 | C2 | semidirect |
| 9. C53×#2138 | C2 | semidirect |
| 16. C2×#13133160 | C22 | semidirect |
| 19. C2×#13133158 | C22 | semidirect |
| 22. #16811008 | C22 | semidirect |
| 23. #16810998 | C22 | semidirect |
| 25. #16810705 | C22 | semidirect |
| 28. #16810441 | C22 | semidirect |
| 29. #16810423 | C22 | semidirect |
| 33. C53×#358 | C22 | semidirect |
| 34. C53×#357 | C22 | semidirect |
| 44. C2×D424 | D4 | semidirect |
| 184. #2138 | D53 | semidirect |
| 213. #358 | C2×D53 | semidirect |
| 215. #357 | C2×D53 | semidirect |
| 216. C53 | #33585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811058 | 2 |
| C22×D848 | 2 |
| #20285202 | 2 |
| #20283566 | 2 |
| #20276773 | 2 |
| #20276749 | 2 |
| #20276473 | 2 |
| #20276430 | 2 |
| C53×#2138 | 2 |
| #33585 | 53 |