Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
488 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 488 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. #19152146 | C2 | semidirect |
| 2. C4×D4×D89 | C2 | semidirect |
| 3. #19151915 | C2 | semidirect |
| 4. #19151889 | C2 | semidirect |
| 5. #19151888 | C2 | semidirect |
| 6. #19151790 | C2 | semidirect |
| 7. #19151730 | C2 | semidirect |
| 8. #19151710 | C2 | semidirect |
| 9. #19151707 | C2 | semidirect |
| 10. #19151654 | C2 | semidirect |
| 11. #459×C89 | C2 | semidirect |
| 16. #15668012 | C22 | semidirect |
| 23. D4×Dic89 | C22 | semidirect |
| 30. #15667944 | C22 | semidirect |
| 31. #15667943 | C22 | semidirect |
| 32. C4⋊#10623494 | C22 | semidirect |
| 35. #15667933 | C22 | semidirect |
| 37. #15667922 | C22 | semidirect |
| 39. #127×C89 | C22 | semidirect |
| 41. C4⋊C8×C89 | C22 | semidirect |
| 42. #102×C89 | C22 | semidirect |
| 96. D4×C89 | #41 | semidirect |
| 112. D356 | #41 | semidirect |
| 155. C89 | #3109 | semidirect |
| 162. #459 | D89 | semidirect |
| 173. #127 | C2×D89 | semidirect |
| 191. C4⋊C8 | C2×D89 | semidirect |
| 195. #102 | C2×D89 | semidirect |
| 256. D4 | #13083573 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152146 | 2 |
| C4×D4×D89 | 2 |
| #19151915 | 2 |
| #19151889 | 2 |
| #19151888 | 2 |
| #19151790 | 2 |
| #19151730 | 2 |
| #19151710 | 2 |
| #19151707 | 2 |
| #19151654 | 2 |
| #459×C89 | 2 |
| #3109 | 89 |