Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#15668038 | C2 | semidirect |
| 2. C22×#13083559 | C2 | semidirect |
| 3. #19152167 | C2 | semidirect |
| 4. #19151813 | C2 | semidirect |
| 5. #19151793 | C2 | semidirect |
| 6. #19151625 | C2 | semidirect |
| 7. #19151602 | C2 | semidirect |
| 8. #19151592 | C2 | semidirect |
| 9. #518×C89 | C2 | semidirect |
| 13. C2×#13083562 | C22 | semidirect |
| 16. C2×#13083559 | C22 | semidirect |
| 19. #15668009 | C22 | semidirect |
| 20. #15668000 | C22 | semidirect |
| 23. C4⋊#10623494 | C22 | semidirect |
| 24. #15667935 | C22 | semidirect |
| 25. #15667932 | C22 | semidirect |
| 26. #15667932 | C22 | semidirect |
| 29. C4×D4×C89 | C22 | semidirect |
| 56. C2×D4×C89 | D4 | semidirect |
| 122. C89 | #3041 | semidirect |
| 126. #518 | D89 | semidirect |
| 147. C4×D4 | C2×D89 | semidirect |
| 169. C2×D4 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668038 | 2 |
| C22×#13083559 | 2 |
| #19152167 | 2 |
| #19151813 | 2 |
| #19151793 | 2 |
| #19151625 | 2 |
| #19151602 | 2 |
| #19151592 | 2 |
| #518×C89 | 2 |
| #3041 | 89 |