Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
472 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 127 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. #20287852 | C2 | semidirect |
| 2. #20277028 | C2 | semidirect |
| 3. #20277026 | C2 | semidirect |
| 4. #20277024 | C2 | semidirect |
| 5. #20277021 | C2 | semidirect |
| 6. D32×D53 | C2 | semidirect |
| 7. #20277008 | C2 | semidirect |
| 8. C2×C53×D32 | C2 | semidirect |
| 12. #16811055 | C22 | semidirect |
| 13. #16811052 | C22 | semidirect |
| 14. D16×D53 | C22 | semidirect |
| 16. Dic848 | C22 | semidirect |
| 17. #16810462 | C22 | semidirect |
| 18. #16810461 | C22 | semidirect |
| 19. D1696 | C22 | semidirect |
| 20. #16810458 | C22 | semidirect |
| 21. #16810457 | C22 | semidirect |
| 22. #16810456 | C22 | semidirect |
| 23. C32×D53 | C22 | semidirect |
| 24. C2×D16×C53 | C22 | semidirect |
| 25. C53×D32 | C22 | semidirect |
| 26. C53×D32 | C22 | semidirect |
| 27. C2×C32×C53 | C22 | semidirect |
| 108. C2×D32 | D53 | semidirect |
| 121. C2×D16 | C2×D53 | semidirect |
| 128. D32 | C2×D53 | semidirect |
| 129. D32 | C2×D53 | semidirect |
| 133. C2×C32 | C2×D53 | semidirect |
| 134. C53 | #33982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287852 | 2 |
| #20277028 | 2 |
| #20277026 | 2 |
| #20277024 | 2 |
| #20277021 | 2 |
| D32×D53 | 2 |
| #20277008 | 2 |
| C2×C53×D32 | 2 |
| #33982 | 53 |