Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 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. #19152153 | C2 | semidirect |
| 3. #19151932 | C2 | semidirect |
| 4. #19151879 | C2 | semidirect |
| 5. #19151878 | C2 | semidirect |
| 6. #19151800 | C2 | semidirect |
| 8. #19151701 | C2 | semidirect |
| 9. #19151699 | C2 | semidirect |
| 10. #19151654 | C2 | semidirect |
| 11. #461×C89 | C2 | semidirect |
| 15. #15668012 | C22 | semidirect |
| 19. Q8×Dic89 | C22 | semidirect |
| 30. #15667946 | C22 | semidirect |
| 31. #15667945 | C22 | semidirect |
| 32. C4⋊#10623494 | C22 | semidirect |
| 33. #15667936 | C22 | semidirect |
| 37. #15667922 | C22 | semidirect |
| 39. C4⋊Q8×C89 | C22 | semidirect |
| 41. C4⋊C8×C89 | C22 | semidirect |
| 42. #103×C89 | C22 | semidirect |
| 147. C89 | #3110 | semidirect |
| 154. #461 | D89 | semidirect |
| 164. C4⋊Q8 | C2×D89 | semidirect |
| 183. C4⋊C8 | C2×D89 | semidirect |
| 185. #103 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152153 | 2 |
| C4×D4×D89 | 2 |
| #19151932 | 2 |
| #19151879 | 2 |
| #19151878 | 2 |
| #19151800 | 2 |
| #19151747 | 2 |
| #19151701 | 2 |
| #19151699 | 2 |
| #19151654 | 2 |
| #461×C89 | 2 |
| #3110 | 89 |