Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
424 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 113 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. #19152111 | C2 | semidirect |
| 2. #19151938 | C2 | semidirect |
| 3. #19151925 | C2 | semidirect |
| 4. #19151834 | C2 | semidirect |
| 5. #19151829 | C2 | semidirect |
| 6. #19151759 | C2 | semidirect |
| 7. #19151746 | C2 | semidirect |
| 8. C2×#15667924 | C2 | semidirect |
| 9. #467×C89 | C2 | semidirect |
| 12. C2×#13083561 | C22 | semidirect |
| 13. C2×D712 | C22 | semidirect |
| 23. #15667946 | C22 | semidirect |
| 24. #15667943 | C22 | semidirect |
| 25. #15667936 | C22 | semidirect |
| 26. #15667934 | C22 | semidirect |
| 27. #15667932 | C22 | semidirect |
| 30. C2×Q16×C89 | C22 | semidirect |
| 33. #107×C89 | C22 | semidirect |
| 34. #103×C89 | C22 | semidirect |
| 122. C89 | #3191 | semidirect |
| 126. #467 | D89 | semidirect |
| 134. C2×Q16 | C2×D89 | semidirect |
| 149. #107 | C2×D89 | semidirect |
| 152. #103 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152111 | 2 |
| #19151938 | 2 |
| #19151925 | 2 |
| #19151834 | 2 |
| #19151829 | 2 |
| #19151759 | 2 |
| #19151746 | 2 |
| C2×#15667924 | 2 |
| #467×C89 | 2 |
| #3191 | 89 |