Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
490 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 490 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×#15668043 | C2 | semidirect |
| 2. C22×#13083561 | C2 | semidirect |
| 4. #19151820 | C2 | semidirect |
| 5. #19151798 | C2 | semidirect |
| 6. #19151625 | C2 | semidirect |
| 7. #19151602 | C2 | semidirect |
| 8. #19151592 | C2 | semidirect |
| 9. #519×C89 | C2 | semidirect |
| 13. C2×#13083564 | C22 | semidirect |
| 16. C2×#13083561 | C22 | semidirect |
| 23. C4⋊#10623494 | C22 | semidirect |
| 24. #15667935 | C22 | semidirect |
| 26. #15667932 | C22 | semidirect |
| 29. C4×Q8×C89 | C22 | semidirect |
| 55. C2×Q8×C89 | D4 | semidirect |
| 117. C89 | #3043 | semidirect |
| 121. #519 | D89 | semidirect |
| 142. C4×Q8 | C2×D89 | semidirect |
| 156. C2×Q8 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668043 | 2 |
| C22×#13083561 | 2 |
| #19152167 | 2 |
| #19151820 | 2 |
| #19151798 | 2 |
| #19151625 | 2 |
| #19151602 | 2 |
| #19151592 | 2 |
| #519×C89 | 2 |
| #3043 | 89 |