Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
490 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 115 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. #19152130 | C2 | semidirect |
| 3. #19151986 | C2 | semidirect |
| 4. #19151961 | C2 | semidirect |
| 5. #19151799 | C2 | semidirect |
| 6. #19151795 | C2 | semidirect |
| 7. #19151793 | C2 | semidirect |
| 8. #19151750 | C2 | semidirect |
| 9. #19151730 | C2 | semidirect |
| 10. #19151654 | C2 | semidirect |
| 11. #459×C89 | C2 | semidirect |
| 15. C2×#13083563 | C22 | semidirect |
| 16. C2×#13083562 | C22 | semidirect |
| 17. C2×#13083559 | C22 | semidirect |
| 23. #15668003 | C22 | semidirect |
| 24. #15667999 | C22 | semidirect |
| 28. C4×Dic178 | C22 | semidirect |
| 32. C4⋊#10623494 | C22 | semidirect |
| 33. #15667934 | C22 | semidirect |
| 34. #15667933 | C22 | semidirect |
| 35. #15667932 | C22 | semidirect |
| 37. #15667922 | C22 | semidirect |
| 38. C2×D8×C89 | C22 | semidirect |
| 40. C4×D4×C89 | C22 | semidirect |
| 41. C4⋊C8×C89 | C22 | semidirect |
| 42. #102×C89 | C22 | semidirect |
| 157. C89 | #3217 | semidirect |
| 165. #459 | D89 | semidirect |
| 175. C2×D8 | C2×D89 | semidirect |
| 189. C4×D4 | C2×D89 | semidirect |
| 193. C4⋊C8 | C2×D89 | semidirect |
| 197. #102 | 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 |
| #19152130 | 2 |
| #19151986 | 2 |
| #19151961 | 2 |
| #19151799 | 2 |
| #19151795 | 2 |
| #19151793 | 2 |
| #19151750 | 2 |
| #19151730 | 2 |
| #19151654 | 2 |
| #459×C89 | 2 |
| #3217 | 89 |