Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15668058 | C2 | semidirect |
| 2. C2×#15668037 | C2 | semidirect |
| 3. C22×D712 | C2 | semidirect |
| 4. #19152167 | C2 | semidirect |
| 5. #19151746 | C2 | semidirect |
| 6. #19151733 | C2 | semidirect |
| 7. #19151602 | C2 | semidirect |
| 8. #19151564 | C2 | semidirect |
| 9. #416×C89 | C2 | semidirect |
| 12. C2×#13083575 | C22 | semidirect |
| 17. C22×D356 | C22 | semidirect |
| 19. C2×D4×D89 | C22 | semidirect |
| 21. C2×#13083561 | C22 | semidirect |
| 23. C2×D712 | C22 | semidirect |
| 24. C2×#13083559 | C22 | semidirect |
| 25. C2×#13083558 | C22 | semidirect |
| 28. #15667987 | C22 | semidirect |
| 30. #15667932 | C22 | semidirect |
| 31. #15667924 | C22 | semidirect |
| 33. C22×C8×C89 | C22 | semidirect |
| 34. #117×C89 | C22 | semidirect |
| 35. #103×C89 | C22 | semidirect |
| 36. #102×C89 | C22 | semidirect |
| 55. C2×D356 | D4 | semidirect |
| 72. #41×C89 | D4 | semidirect |
| 152. C89 | #3008 | semidirect |
| 160. #416 | D89 | semidirect |
| 179. C22×C8 | C2×D89 | semidirect |
| 184. #117 | C2×D89 | semidirect |
| 185. #103 | C2×D89 | semidirect |
| 187. #102 | C2×D89 | semidirect |
| 198. #41 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668058 | 2 |
| C2×#15668037 | 2 |
| C22×D712 | 2 |
| #19152167 | 2 |
| #19151746 | 2 |
| #19151733 | 2 |
| #19151602 | 2 |
| #19151564 | 2 |
| #416×C89 | 2 |
| #3008 | 89 |