Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
460 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 123 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. D4×D356 | C2 | semidirect |
| 2. #19151946 | C2 | semidirect |
| 3. #19151922 | C2 | semidirect |
| 4. #19151885 | C2 | semidirect |
| 5. #19151849 | C2 | semidirect |
| 6. #19151793 | C2 | semidirect |
| 7. #19151731 | C2 | semidirect |
| 8. C4×#13083559 | C2 | semidirect |
| 9. #19151676 | C2 | semidirect |
| 10. #19151602 | C2 | semidirect |
| 11. #555×C89 | C2 | semidirect |
| 15. C2×#13083559 | C22 | semidirect |
| 16. C2×#13083558 | C22 | semidirect |
| 22. #15667945 | C22 | semidirect |
| 23. #15667943 | C22 | semidirect |
| 24. C4⋊#10623494 | C22 | semidirect |
| 25. #15667933 | C22 | semidirect |
| 28. #15667932 | C22 | semidirect |
| 29. #15667932 | C22 | semidirect |
| 30. #15667932 | C22 | semidirect |
| 31. C22⋊#10623494 | C22 | semidirect |
| 32. C4×#10623494 | C22 | semidirect |
| 33. C4⋊Q8×C89 | C22 | semidirect |
| 36. #121×C89 | C22 | semidirect |
| 38. C4×D4×C89 | C22 | semidirect |
| 40. #117×C89 | C22 | semidirect |
| 141. C89 | #3325 | semidirect |
| 142. #555 | D89 | semidirect |
| 158. C4⋊Q8 | C2×D89 | semidirect |
| 164. #121 | C2×D89 | semidirect |
| 168. C4×D4 | C2×D89 | semidirect |
| 170. #117 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D356 | 2 |
| #19151946 | 2 |
| #19151922 | 2 |
| #19151885 | 2 |
| #19151849 | 2 |
| #19151793 | 2 |
| #19151731 | 2 |
| C4×#13083559 | 2 |
| #19151676 | 2 |
| #19151602 | 2 |
| #555×C89 | 2 |
| #3325 | 89 |