Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15668038 | C2 | semidirect |
| 2. C2×#15668019 | C2 | semidirect |
| 3. #19152176 | C2 | semidirect |
| 4. #19151849 | C2 | semidirect |
| 5. #19151842 | C2 | semidirect |
| 6. #19151832 | C2 | semidirect |
| 7. #19151825 | C2 | semidirect |
| 8. #19151641 | C2 | semidirect |
| 9. #19151592 | C2 | semidirect |
| 10. C2×#15667933 | C2 | semidirect |
| 11. #535×C89 | C2 | semidirect |
| 18. C2×#13083558 | C22 | semidirect |
| 20. C22×#10623494 | C22 | semidirect |
| 21. #15667991 | C22 | semidirect |
| 23. #15667986 | C22 | semidirect |
| 27. #15667945 | C22 | semidirect |
| 28. #15667943 | C22 | semidirect |
| 29. #15667935 | C22 | semidirect |
| 30. #15667935 | C22 | semidirect |
| 33. #15667932 | C22 | semidirect |
| 34. #15667932 | C22 | semidirect |
| 54. #13083558 | D4 | semidirect |
| 152. C89 | #3062 | semidirect |
| 156. #535 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668038 | 2 |
| C2×#15668019 | 2 |
| #19152176 | 2 |
| #19151849 | 2 |
| #19151842 | 2 |
| #19151832 | 2 |
| #19151825 | 2 |
| #19151641 | 2 |
| #19151592 | 2 |
| C2×#15667933 | 2 |
| #535×C89 | 2 |
| #3062 | 89 |