Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
418 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 121 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. #19152072 | C2 | semidirect |
| 2. #19151919 | C2 | semidirect |
| 3. #19151895 | C2 | semidirect |
| 4. #19151790 | C2 | semidirect |
| 5. #19151731 | C2 | semidirect |
| 6. #19151708 | C2 | semidirect |
| 7. C4×#13083559 | C2 | semidirect |
| 8. #19151659 | C2 | semidirect |
| 9. #540×C89 | C2 | semidirect |
| 18. #15667945 | C22 | semidirect |
| 19. #15667943 | C22 | semidirect |
| 20. C4⋊#10623494 | C22 | semidirect |
| 21. #15667933 | C22 | semidirect |
| 22. #15667933 | C22 | semidirect |
| 26. #15667923 | C22 | semidirect |
| 27. C4×#10623494 | C22 | semidirect |
| 28. #127×C89 | C22 | semidirect |
| 29. #125×C89 | C22 | semidirect |
| 33. C4×D4×C89 | C22 | semidirect |
| 109. C89 | #3122 | semidirect |
| 110. #540 | D89 | semidirect |
| 122. #127 | C2×D89 | semidirect |
| 123. #125 | C2×D89 | semidirect |
| 130. C4×D4 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152072 | 2 |
| #19151919 | 2 |
| #19151895 | 2 |
| #19151790 | 2 |
| #19151731 | 2 |
| #19151708 | 2 |
| C4×#13083559 | 2 |
| #19151659 | 2 |
| #540×C89 | 2 |
| #3122 | 89 |