Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15668040 | C2 | semidirect |
| 2. C2×#15668020 | C2 | semidirect |
| 3. #19152179 | C2 | semidirect |
| 4. #19152167 | C2 | semidirect |
| 5. #19151852 | C2 | semidirect |
| 6. #19151845 | C2 | semidirect |
| 7. #19151835 | C2 | semidirect |
| 8. #19151828 | C2 | semidirect |
| 9. #19151592 | C2 | semidirect |
| 10. C2×#15667932 | C2 | semidirect |
| 11. #428×C89 | C2 | semidirect |
| 19. C2×#13083557 | C22 | semidirect |
| 21. C2×C8×D89 | C22 | semidirect |
| 25. #15667992 | C22 | semidirect |
| 29. #15667987 | C22 | semidirect |
| 32. #15667935 | C22 | semidirect |
| 33. #15667935 | C22 | semidirect |
| 36. #15667932 | C22 | semidirect |
| 37. #15667932 | C22 | semidirect |
| 41. #107×C89 | C22 | semidirect |
| 42. #106×C89 | C22 | semidirect |
| 77. M16×C89 | D4 | semidirect |
| 152. C89 | #3062 | semidirect |
| 161. #428 | D89 | semidirect |
| 187. #107 | C2×D89 | semidirect |
| 188. #106 | C2×D89 | semidirect |
| 220. M16 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668040 | 2 |
| C2×#15668020 | 2 |
| #19152179 | 2 |
| #19152167 | 2 |
| #19151852 | 2 |
| #19151845 | 2 |
| #19151835 | 2 |
| #19151828 | 2 |
| #19151592 | 2 |
| C2×#15667932 | 2 |
| #428×C89 | 2 |
| #3062 | 89 |