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. #20287856 | C2 | semidirect |
| 2. #20277033 | C2 | semidirect |
| 3. #20277027 | C2 | semidirect |
| 4. #20277022 | C2 | semidirect |
| 5. C2×#16810460 | C2 | semidirect |
| 6. #20277009 | C2 | semidirect |
| 7. C53×#3417 | C2 | semidirect |
| 12. #16810463 | C22 | semidirect |
| 13. #16810461 | C22 | semidirect |
| 14. #16810460 | C22 | semidirect |
| 15. #16810460 | C22 | semidirect |
| 16. #16810458 | C22 | semidirect |
| 17. #16810457 | C22 | semidirect |
| 18. C2×#13133123 | C22 | semidirect |
| 21. C53×#508 | C22 | semidirect |
| 22. C2×Q32×C53 | C22 | semidirect |
| 92. #3417 | D53 | semidirect |
| 108. #508 | C2×D53 | semidirect |
| 109. C2×Q32 | 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 |
|---|---|
| #20287856 | 2 |
| #20277033 | 2 |
| #20277027 | 2 |
| #20277022 | 2 |
| C2×#16810460 | 2 |
| #20277009 | 2 |
| C53×#3417 | 2 |
| #33983 | 53 |