Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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. C22×#13083561 | C2 | semidirect |
| 2. C2×#15668019 | C2 | semidirect |
| 4. #19151846 | C2 | semidirect |
| 5. #19151829 | C2 | semidirect |
| 6. #19151634 | C2 | semidirect |
| 7. #19151607 | C2 | semidirect |
| 8. #19151602 | C2 | semidirect |
| 9. #536×C89 | C2 | semidirect |
| 16. C2×#13083558 | C22 | semidirect |
| 18. C22×#10623494 | C22 | semidirect |
| 24. #15667945 | C22 | semidirect |
| 25. #15667943 | C22 | semidirect |
| 26. #15667936 | C22 | semidirect |
| 33. C22⋊Q8×C89 | C22 | semidirect |
| 46. C2×#10623494 | D4 | semidirect |
| 121. C89 | #3057 | semidirect |
| 124. #536 | D89 | semidirect |
| 147. C22⋊Q8 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13083561 | 2 |
| C2×#15668019 | 2 |
| #19152162 | 2 |
| #19151846 | 2 |
| #19151829 | 2 |
| #19151634 | 2 |
| #19151607 | 2 |
| #19151602 | 2 |
| #536×C89 | 2 |
| #3057 | 89 |