Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#15668020 | C2 | semidirect |
| 2. #19152176 | C2 | semidirect |
| 3. #19152165 | C2 | semidirect |
| 4. #19151848 | C2 | semidirect |
| 5. #19151841 | C2 | semidirect |
| 6. #19151831 | C2 | semidirect |
| 7. #19151824 | C2 | semidirect |
| 8. #19151640 | C2 | semidirect |
| 9. #19151594 | C2 | semidirect |
| 10. C2×#15667933 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C89 | C2 | semidirect |
| 14. C2×#13083557 | C22 | semidirect |
| 16. C2×C8×D89 | C22 | semidirect |
| 20. #15667988 | C22 | semidirect |
| 25. #15667983 | C22 | semidirect |
| 29. #15667946 | C22 | semidirect |
| 30. #15667944 | C22 | semidirect |
| 31. #15667936 | C22 | semidirect |
| 32. #15667936 | C22 | semidirect |
| 35. #15667933 | C22 | semidirect |
| 36. #15667933 | C22 | semidirect |
| 83. M16×C89 | D4 | semidirect |
| 152. C89 | #3062 | semidirect |
| 153. C2×AGL(1,ℤ/8) | D89 | semidirect |
| 220. M16 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668020 | 2 |
| #19152176 | 2 |
| #19152165 | 2 |
| #19151848 | 2 |
| #19151841 | 2 |
| #19151831 | 2 |
| #19151824 | 2 |
| #19151640 | 2 |
| #19151594 | 2 |
| C2×#15667933 | 2 |
| C2×AGL(1,ℤ/8)×C89 | 2 |
| #3062 | 89 |