Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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×#15668000 | C2 | semidirect |
| 2. #19151985 | C2 | semidirect |
| 3. #19151960 | C2 | semidirect |
| 4. #19151813 | C2 | semidirect |
| 5. #19151736 | C2 | semidirect |
| 6. #19151731 | C2 | semidirect |
| 7. #19151655 | C2 | semidirect |
| 8. #532×C89 | C2 | semidirect |
| 11. C2×#13083562 | C22 | semidirect |
| 19. C4⋊#10623494 | C22 | semidirect |
| 20. #15667935 | C22 | semidirect |
| 23. #15667923 | C22 | semidirect |
| 25. C4⋊Q8×C89 | C22 | semidirect |
| 26. #127×C89 | C22 | semidirect |
| 31. C4×D4×C89 | C22 | semidirect |
| 121. C89 | #3213 | semidirect |
| 122. #532 | D89 | semidirect |
| 135. C4⋊Q8 | C2×D89 | semidirect |
| 136. #127 | C2×D89 | semidirect |
| 145. C4×D4 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668000 | 2 |
| #19151985 | 2 |
| #19151960 | 2 |
| #19151813 | 2 |
| #19151736 | 2 |
| #19151731 | 2 |
| #19151655 | 2 |
| #532×C89 | 2 |
| #3213 | 89 |