Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
488 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 121 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. #19152149 | C2 | semidirect |
| 2. C4×D4×D89 | C2 | semidirect |
| 3. #19151918 | C2 | semidirect |
| 4. #19151885 | C2 | semidirect |
| 5. #19151794 | C2 | semidirect |
| 6. #19151793 | C2 | semidirect |
| 7. #19151733 | C2 | semidirect |
| 8. #19151709 | C2 | semidirect |
| 9. #19151707 | C2 | semidirect |
| 10. #19151654 | C2 | semidirect |
| 11. #476×C89 | C2 | semidirect |
| 17. #15668009 | C22 | semidirect |
| 25. #15667974 | C22 | semidirect |
| 31. #15667943 | C22 | semidirect |
| 32. C4⋊#10623494 | C22 | semidirect |
| 33. #15667934 | C22 | semidirect |
| 35. #15667932 | C22 | semidirect |
| 37. #15667922 | C22 | semidirect |
| 38. C4⋊Q8×C89 | C22 | semidirect |
| 40. #106×C89 | C22 | semidirect |
| 41. C4⋊C8×C89 | C22 | semidirect |
| 93. D4×C89 | #41 | semidirect |
| 112. D356 | #41 | semidirect |
| 155. C89 | #3109 | semidirect |
| 160. #476 | D89 | semidirect |
| 172. C4⋊Q8 | C2×D89 | semidirect |
| 189. #106 | C2×D89 | semidirect |
| 191. C4⋊C8 | C2×D89 | semidirect |
| 256. D4 | #13083575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152149 | 2 |
| C4×D4×D89 | 2 |
| #19151918 | 2 |
| #19151885 | 2 |
| #19151794 | 2 |
| #19151793 | 2 |
| #19151733 | 2 |
| #19151709 | 2 |
| #19151707 | 2 |
| #19151654 | 2 |
| #476×C89 | 2 |
| #3109 | 89 |