Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
490 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 113 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. #127×D89 | C2 | semidirect |
| 2. #19152127 | C2 | semidirect |
| 3. #19151988 | C2 | semidirect |
| 4. #19151963 | C2 | semidirect |
| 5. #19151962 | C2 | semidirect |
| 6. #19151796 | C2 | semidirect |
| 7. #19151791 | C2 | semidirect |
| 8. #19151747 | C2 | semidirect |
| 9. #19151730 | C2 | semidirect |
| 10. #19151653 | C2 | semidirect |
| 11. #496×C89 | C2 | semidirect |
| 15. C2×#13083561 | C22 | semidirect |
| 16. C2×#13083559 | C22 | semidirect |
| 22. #15668004 | C22 | semidirect |
| 26. Q8×Dic89 | C22 | semidirect |
| 27. D4×Dic89 | C22 | semidirect |
| 31. #15667941 | C22 | semidirect |
| 32. #15667934 | C22 | semidirect |
| 33. #15667934 | C22 | semidirect |
| 34. #15667933 | C22 | semidirect |
| 35. #15667933 | C22 | semidirect |
| 37. #15667923 | C22 | semidirect |
| 38. C2×SD16×C89 | C22 | semidirect |
| 39. C2×D8×C89 | C22 | semidirect |
| 41. #124×C89 | C22 | semidirect |
| 42. #97×C89 | C22 | semidirect |
| 153. C89 | #3217 | semidirect |
| 157. #496 | D89 | semidirect |
| 169. C2×SD16 | C2×D89 | semidirect |
| 171. C2×D8 | C2×D89 | semidirect |
| 179. #124 | C2×D89 | semidirect |
| 195. #97 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #127×D89 | 2 |
| #19152127 | 2 |
| #19151988 | 2 |
| #19151963 | 2 |
| #19151962 | 2 |
| #19151796 | 2 |
| #19151791 | 2 |
| #19151747 | 2 |
| #19151730 | 2 |
| #19151653 | 2 |
| #496×C89 | 2 |
| #3217 | 89 |