Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
806 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 153 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×#15668038 | C2 | semidirect |
| 3. #19151741 | C2 | semidirect |
| 4. #19151736 | C2 | semidirect |
| 5. #19151731 | C2 | semidirect |
| 6. #19151597 | C2 | semidirect |
| 7. #19151562 | C2 | semidirect |
| 8. C2×#121×C89 | C2 | semidirect |
| 13. C2×#13083574 | C22 | semidirect |
| 14. C22×Dic178 | C22 | semidirect |
| 15. C22×D356 | C22 | semidirect |
| 19. C2×#13083562 | C22 | semidirect |
| 20. C2×#13083559 | C22 | semidirect |
| 21. C2×#13083558 | C22 | semidirect |
| 22. #15667935 | C22 | semidirect |
| 23. #15667932 | C22 | semidirect |
| 24. C22⋊#10623494 | C22 | semidirect |
| 25. C22⋊#10623494 | C22 | semidirect |
| 27. C22×D4×C89 | C22 | semidirect |
| 32. #121×C89 | C22 | semidirect |
| 33. C2×C4⋊C4×C89 | C22 | semidirect |
| 41. #13083574 | D4 | semidirect |
| 115. D356 | C2×D4 | semidirect |
| 120. Dic178 | C2×D4 | semidirect |
| 135. C22×C89 | AGL(1,ℤ/8) | semidirect |
| 156. C89 | #3006 | semidirect |
| 159. C2×#121 | D89 | semidirect |
| 174. C22×D4 | C2×D89 | semidirect |
| 184. #121 | C2×D89 | semidirect |
| 185. C2×C4⋊C4 | C2×D89 | semidirect |
| 295. C22 | #15668038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13083574 | 2 |
| C2×#15668038 | 2 |
| #19151741 | 2 |
| #19151736 | 2 |
| #19151731 | 2 |
| #19151597 | 2 |
| #19151562 | 2 |
| C2×#121×C89 | 2 |
| #3006 | 89 |