Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
596 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 137 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×#15668036 | C2 | semidirect |
| 2. C2×#15668031 | C2 | semidirect |
| 3. C2×D8×D89 | C2 | semidirect |
| 4. #19152161 | C2 | semidirect |
| 5. #19151986 | C2 | semidirect |
| 6. #19151985 | C2 | semidirect |
| 7. #19151982 | C2 | semidirect |
| 8. #19151981 | C2 | semidirect |
| 9. #19151973 | C2 | semidirect |
| 10. #19151552 | C2 | semidirect |
| 11. #493×C89 | C2 | semidirect |
| 16. C2×Dic356 | C22 | semidirect |
| 17. C2×#13083563 | C22 | semidirect |
| 18. C2×#13083562 | C22 | semidirect |
| 19. C2×#13083562 | C22 | semidirect |
| 22. C2×#13083559 | C22 | semidirect |
| 26. #15668008 | C22 | semidirect |
| 27. #15668000 | C22 | semidirect |
| 28. #15667999 | C22 | semidirect |
| 32. #15667923 | C22 | semidirect |
| 33. #15667922 | C22 | semidirect |
| 34. C8×Dic89 | C22 | semidirect |
| 36. C2×D8×C89 | C22 | semidirect |
| 37. C2×D8×C89 | C22 | semidirect |
| 38. #127×C89 | C22 | semidirect |
| 39. C4×C8×C89 | C22 | semidirect |
| 59. #13083557 | D4 | semidirect |
| 62. C8×D89 | D4 | semidirect |
| 130. C89 | #3155 | semidirect |
| 140. #493 | D89 | semidirect |
| 155. C2×D8 | C2×D89 | semidirect |
| 156. C2×D8 | C2×D89 | semidirect |
| 160. #127 | C2×D89 | semidirect |
| 169. C4×C8 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668036 | 2 |
| C2×#15668031 | 2 |
| C2×D8×D89 | 2 |
| #19152161 | 2 |
| #19151986 | 2 |
| #19151985 | 2 |
| #19151982 | 2 |
| #19151981 | 2 |
| #19151973 | 2 |
| #19151552 | 2 |
| #493×C89 | 2 |
| #3155 | 89 |