Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
462 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 151 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. #20287868 | C2 | semidirect |
| 2. #20287856 | C2 | semidirect |
| 3. #20277035 | C2 | semidirect |
| 4. #20277030 | C2 | semidirect |
| 5. #20277024 | C2 | semidirect |
| 6. C2×#16810462 | C2 | semidirect |
| 7. C53×#2258 | C2 | semidirect |
| 13. #16811055 | C22 | semidirect |
| 14. C2×Dic424 | C22 | semidirect |
| 16. Dic848 | C22 | semidirect |
| 17. #16810462 | C22 | semidirect |
| 18. #16810462 | C22 | semidirect |
| 19. #16810462 | C22 | semidirect |
| 20. D1696 | C22 | semidirect |
| 22. C53×M64 | C22 | semidirect |
| 23. C2×C32×C53 | C22 | semidirect |
| 98. #2258 | D53 | semidirect |
| 117. M64 | C2×D53 | semidirect |
| 118. C2×C32 | C2×D53 | semidirect |
| 119. C53 | #33983 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287868 | 2 |
| #20287856 | 2 |
| #20277035 | 2 |
| #20277030 | 2 |
| #20277024 | 2 |
| C2×#16810462 | 2 |
| C53×#2258 | 2 |
| #33983 | 53 |