Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
410 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 410 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 |
|---|---|---|
| 2. #19151936 | C2 | semidirect |
| 3. #19151922 | C2 | semidirect |
| 4. #19151846 | C2 | semidirect |
| 5. #19151829 | C2 | semidirect |
| 6. #19151748 | C2 | semidirect |
| 7. #19151737 | C2 | semidirect |
| 8. #19151565 | C2 | semidirect |
| 9. #536×C89 | C2 | semidirect |
| 13. C2×#13083558 | C22 | semidirect |
| 14. C22×#10623494 | C22 | semidirect |
| 22. #15667945 | C22 | semidirect |
| 23. #15667943 | C22 | semidirect |
| 24. #15667936 | C22 | semidirect |
| 25. #15667936 | C22 | semidirect |
| 29. C22⋊#10623494 | C22 | semidirect |
| 31. C22×Q8×C89 | C22 | semidirect |
| 37. C22⋊Q8×C89 | C22 | semidirect |
| 38. #117×C89 | C22 | semidirect |
| 138. C89 | #3200 | semidirect |
| 139. #536 | D89 | semidirect |
| 149. C22×Q8 | C2×D89 | semidirect |
| 162. C22⋊Q8 | C2×D89 | semidirect |
| 168. #117 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152162 | 2 |
| #19151936 | 2 |
| #19151922 | 2 |
| #19151846 | 2 |
| #19151829 | 2 |
| #19151748 | 2 |
| #19151737 | 2 |
| #19151565 | 2 |
| #536×C89 | 2 |
| #3200 | 89 |