Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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. C22×#13083559 | C2 | semidirect |
| 2. #19152162 | C2 | semidirect |
| 3. #19152073 | C2 | semidirect |
| 4. #19151815 | C2 | semidirect |
| 5. #19151791 | C2 | semidirect |
| 6. #19151626 | C2 | semidirect |
| 7. #19151604 | C2 | semidirect |
| 8. #19151594 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C89 | C2 | semidirect |
| 14. #15668008 | C22 | semidirect |
| 15. #15668001 | C22 | semidirect |
| 19. D4×Dic89 | C22 | semidirect |
| 23. #15667941 | C22 | semidirect |
| 24. #15667936 | C22 | semidirect |
| 25. #15667934 | C22 | semidirect |
| 26. #15667933 | C22 | semidirect |
| 30. C2×SD16×C89 | C22 | semidirect |
| 31. C2×D8×C89 | C22 | semidirect |
| 58. C2×D4×C89 | D4 | semidirect |
| 122. C89 | #3041 | semidirect |
| 123. C2×AGL(1,ℤ/8) | D89 | semidirect |
| 136. C2×SD16 | C2×D89 | semidirect |
| 139. C2×D8 | C2×D89 | semidirect |
| 168. C2×D4 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13083559 | 2 |
| #19152162 | 2 |
| #19152073 | 2 |
| #19151815 | 2 |
| #19151791 | 2 |
| #19151626 | 2 |
| #19151604 | 2 |
| #19151594 | 2 |
| C2×AGL(1,ℤ/8)×C89 | 2 |
| #3041 | 89 |