Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #19152210 | C2 | semidirect |
| 2. #19151993 | C2 | semidirect |
| 3. #19151970 | C2 | semidirect |
| 4. #19151962 | C2 | semidirect |
| 5. #19151952 | C2 | semidirect |
| 6. #19151817 | C2 | semidirect |
| 7. #19151795 | C2 | semidirect |
| 8. #19151760 | C2 | semidirect |
| 9. #19151749 | C2 | semidirect |
| 10. #19151659 | C2 | semidirect |
| 12. C2×#13083564 | C22 | semidirect |
| 15. C2×#13083562 | C22 | semidirect |
| 16. #15668012 | C22 | semidirect |
| 18. #15668004 | C22 | semidirect |
| 21. C4×Dic178 | C22 | semidirect |
| 22. C4⋊#10623494 | C22 | semidirect |
| 23. #15667936 | C22 | semidirect |
| 26. #15667933 | C22 | semidirect |
| 28. #15667923 | C22 | semidirect |
| 29. C4×#10623494 | C22 | semidirect |
| 123. C89 | #3222 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152210 | 2 |
| #19151993 | 2 |
| #19151970 | 2 |
| #19151962 | 2 |
| #19151952 | 2 |
| #19151817 | 2 |
| #19151795 | 2 |
| #19151760 | 2 |
| #19151749 | 2 |
| #19151659 | 2 |
| #535×C89 | 2 |
| #3222 | 89 |