Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
656 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 145 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×#15668039 | C2 | semidirect |
| 2. #19152149 | C2 | semidirect |
| 3. #127×D89 | C2 | semidirect |
| 4. #19151984 | C2 | semidirect |
| 5. #19151975 | C2 | semidirect |
| 6. #19151974 | C2 | semidirect |
| 7. #19151972 | C2 | semidirect |
| 8. C4×#13083557 | C2 | semidirect |
| 9. #492×C89 | C2 | semidirect |
| 14. C2×#13083561 | C22 | semidirect |
| 15. C2×D712 | C22 | semidirect |
| 16. C2×#13083559 | C22 | semidirect |
| 19. #15668009 | C22 | semidirect |
| 22. #15668001 | C22 | semidirect |
| 26. #15667922 | C22 | semidirect |
| 27. C4×#10623494 | C22 | semidirect |
| 28. C2×SD16×C89 | C22 | semidirect |
| 29. C4⋊Q8×C89 | C22 | semidirect |
| 31. C4×C8×C89 | C22 | semidirect |
| 49. #13083557 | D4 | semidirect |
| 85. C8×C89 | C2×D4 | semidirect |
| 86. #10623494 | C2×D4 | semidirect |
| 98. C4×C89 | AGL(1,ℤ/8) | semidirect |
| 109. C89 | #3151 | semidirect |
| 117. #492 | D89 | semidirect |
| 124. C2×SD16 | C2×D89 | semidirect |
| 128. C4⋊Q8 | C2×D89 | semidirect |
| 140. C4×C8 | C2×D89 | semidirect |
| 195. C8 | D4×D89 | semidirect |
| 209. C4 | #15668039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668039 | 2 |
| #19152149 | 2 |
| #127×D89 | 2 |
| #19151984 | 2 |
| #19151975 | 2 |
| #19151974 | 2 |
| #19151972 | 2 |
| C4×#13083557 | 2 |
| #492×C89 | 2 |
| #3151 | 89 |