Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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. #19152153 | C2 | semidirect |
| 3. #19151960 | C2 | semidirect |
| 4. #19151958 | C2 | semidirect |
| 5. #19151957 | C2 | semidirect |
| 6. #19151954 | C2 | semidirect |
| 7. #19151951 | C2 | semidirect |
| 8. #19151605 | C2 | semidirect |
| 10. #19151550 | C2 | semidirect |
| 11. #489×C89 | C2 | semidirect |
| 15. #15668012 | C22 | semidirect |
| 16. #15668003 | C22 | semidirect |
| 30. #15667937 | C22 | semidirect |
| 31. #15667936 | C22 | semidirect |
| 32. #15667935 | C22 | semidirect |
| 36. #15667923 | C22 | semidirect |
| 37. C8×Dic89 | C22 | semidirect |
| 38. C4⋊Q8×C89 | C22 | semidirect |
| 40. #103×C89 | C22 | semidirect |
| 42. #97×C89 | C22 | semidirect |
| 139. C89 | #3140 | semidirect |
| 145. #489 | D89 | semidirect |
| 155. C4⋊Q8 | C2×D89 | semidirect |
| 174. #103 | C2×D89 | semidirect |
| 180. #97 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152153 | 2 |
| #124×D89 | 2 |
| #19151960 | 2 |
| #19151958 | 2 |
| #19151957 | 2 |
| #19151954 | 2 |
| #19151951 | 2 |
| #19151605 | 2 |
| #19151601 | 2 |
| #19151550 | 2 |
| #489×C89 | 2 |
| #3140 | 89 |