Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 758 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. C22×#13083574 | C2 | semidirect |
| 2. C2×#15668042 | C2 | semidirect |
| 3. C2×#15668037 | C2 | semidirect |
| 4. #19151758 | C2 | semidirect |
| 5. #19151741 | C2 | semidirect |
| 6. #19151606 | C2 | semidirect |
| 7. #19151602 | C2 | semidirect |
| 8. #19151562 | C2 | semidirect |
| 9. #525×C89 | C2 | semidirect |
| 20. C2×#13083564 | C22 | semidirect |
| 21. C2×#13083562 | C22 | semidirect |
| 22. C2×#13083561 | C22 | semidirect |
| 23. C2×#13083559 | C22 | semidirect |
| 26. #15667935 | C22 | semidirect |
| 27. #15667932 | C22 | semidirect |
| 28. C22⋊#10623494 | C22 | semidirect |
| 32. C22⋊Q8×C89 | C22 | semidirect |
| 33. #121×C89 | C22 | semidirect |
| 43. C2×Dic178 | D4 | semidirect |
| 47. C2×D356 | D4 | semidirect |
| 146. C89 | #3005 | semidirect |
| 150. #525 | D89 | semidirect |
| 175. C22⋊Q8 | C2×D89 | semidirect |
| 176. #121 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13083574 | 2 |
| C2×#15668042 | 2 |
| C2×#15668037 | 2 |
| #19151758 | 2 |
| #19151741 | 2 |
| #19151606 | 2 |
| #19151602 | 2 |
| #19151562 | 2 |
| #525×C89 | 2 |
| #3005 | 89 |