Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
556 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 133 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. #19152269 | C2 | semidirect |
| 3. #19151974 | C2 | semidirect |
| 4. #19151849 | C2 | semidirect |
| 5. #19151795 | C2 | semidirect |
| 6. #19151793 | C2 | semidirect |
| 7. #19151741 | C2 | semidirect |
| 8. #19151732 | C2 | semidirect |
| 9. C4×#13083562 | C2 | semidirect |
| 10. #19151676 | C2 | semidirect |
| 11. D42×C89 | C2 | semidirect |
| 12. C2×#13083574 | C22 | semidirect |
| 15. C2×#13083562 | C22 | semidirect |
| 17. C2×#13083559 | C22 | semidirect |
| 18. C2×#13083559 | C22 | semidirect |
| 19. C2×#13083558 | C22 | semidirect |
| 20. #15668009 | C22 | semidirect |
| 22. #15667986 | C22 | semidirect |
| 24. C4×Dic178 | C22 | semidirect |
| 26. #15667943 | C22 | semidirect |
| 27. C4⋊#10623494 | C22 | semidirect |
| 28. #15667935 | C22 | semidirect |
| 30. #15667933 | C22 | semidirect |
| 31. #15667932 | C22 | semidirect |
| 32. C22⋊#10623494 | C22 | semidirect |
| 33. C4×#10623494 | C22 | semidirect |
| 52. #13083562 | D4 | semidirect |
| 117. Dic178 | C2×D4 | semidirect |
| 120. #10623494 | C2×D4 | semidirect |
| 138. C4×C89 | AGL(1,ℤ/8) | semidirect |
| 151. C89 | #3274 | semidirect |
| 154. D42 | D89 | semidirect |
| 291. C4 | #15668038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668038 | 2 |
| #19152269 | 2 |
| #19151974 | 2 |
| #19151849 | 2 |
| #19151795 | 2 |
| #19151793 | 2 |
| #19151741 | 2 |
| #19151732 | 2 |
| C4×#13083562 | 2 |
| #19151676 | 2 |
| D42×C89 | 2 |
| #3274 | 89 |