Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
472 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 115 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. #19152108 | C2 | semidirect |
| 2. C2×#15667987 | C2 | semidirect |
| 3. #19151933 | C2 | semidirect |
| 4. #19151924 | C2 | semidirect |
| 5. #19151833 | C2 | semidirect |
| 6. #19151828 | C2 | semidirect |
| 7. #19151751 | C2 | semidirect |
| 8. #19151744 | C2 | semidirect |
| 9. #19151731 | C2 | semidirect |
| 10. C22⋊C8×D89 | C2 | semidirect |
| 11. #481×C89 | C2 | semidirect |
| 12. C2×#13083573 | C22 | semidirect |
| 16. C2×#13083563 | C22 | semidirect |
| 17. C2×#13083559 | C22 | semidirect |
| 18. C2×C8×D89 | C22 | semidirect |
| 20. #15667992 | C22 | semidirect |
| 26. #15667983 | C22 | semidirect |
| 30. #15667970 | C22 | semidirect |
| 32. #15667945 | C22 | semidirect |
| 33. #15667935 | C22 | semidirect |
| 34. #15667934 | C22 | semidirect |
| 35. #15667932 | C22 | semidirect |
| 37. #15667924 | C22 | semidirect |
| 40. #106×C89 | C22 | semidirect |
| 41. #102×C89 | C22 | semidirect |
| 159. C89 | #3188 | semidirect |
| 164. #481 | D89 | semidirect |
| 194. #106 | C2×D89 | semidirect |
| 198. #102 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152108 | 2 |
| C2×#15667987 | 2 |
| #19151933 | 2 |
| #19151924 | 2 |
| #19151833 | 2 |
| #19151828 | 2 |
| #19151751 | 2 |
| #19151744 | 2 |
| #19151731 | 2 |
| C22⋊C8×D89 | 2 |
| #481×C89 | 2 |
| #3188 | 89 |