Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
718 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 718 conjugacy classes of subgroups — too many to draw. Only its 211 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. #20283566 | C2 | semidirect |
| 3. #20276590 | C2 | semidirect |
| 4. #20276561 | C2 | semidirect |
| 5. #20276430 | C2 | semidirect |
| 6. #20276311 | C2 | semidirect |
| 7. C53×#2158 | C2 | semidirect |
| 10. C2×D848 | C4 | semidirect |
| 15. #16810705 | C22 | semidirect |
| 18. #16810423 | C22 | semidirect |
| 19. #16810398 | C22 | semidirect |
| 20. C16×Dic53 | C22 | semidirect |
| 23. C53×#367 | C22 | semidirect |
| 24. C53×#366 | C22 | semidirect |
| 28. C2×D424 | C2×C4 | semidirect |
| 35. D848 | C2×C4 | semidirect |
| 36. D848 | C2×C4 | semidirect |
| 44. C2×C16×C53 | C2×C4 | semidirect |
| 109. #2158 | D53 | semidirect |
| 128. #367 | C2×D53 | semidirect |
| 129. #366 | C2×D53 | semidirect |
| 133. C53 | #33456 | semidirect |
| 150. C2×C16 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D848 | 2 |
| #20283566 | 2 |
| #20276590 | 2 |
| #20276561 | 2 |
| #20276430 | 2 |
| #20276311 | 2 |
| C53×#2158 | 2 |
| #33456 | 53 |