Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15668045 | C2 | semidirect |
| 2. C2×#15668032 | C2 | semidirect |
| 3. C22×#13083562 | C2 | semidirect |
| 4. #19152169 | C2 | semidirect |
| 5. #19152165 | C2 | semidirect |
| 6. #19151989 | C2 | semidirect |
| 7. #19151986 | C2 | semidirect |
| 8. #19151981 | C2 | semidirect |
| 9. #19151969 | C2 | semidirect |
| 10. #19151556 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C89 | C2 | semidirect |
| 16. C2×Dic356 | C22 | semidirect |
| 17. C2×#13083564 | C22 | semidirect |
| 18. C2×#13083563 | C22 | semidirect |
| 22. C2×#13083562 | C22 | semidirect |
| 23. C2×#13083561 | C22 | semidirect |
| 24. C2×#13083559 | C22 | semidirect |
| 26. #15668010 | C22 | semidirect |
| 29. #15667999 | C22 | semidirect |
| 35. #15667922 | C22 | semidirect |
| 36. C8×Dic89 | C22 | semidirect |
| 63. C2×#10623494 | D4 | semidirect |
| 86. M16×C89 | D4 | semidirect |
| 149. C89 | #3154 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D89 | semidirect |
| 226. M16 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668045 | 2 |
| C2×#15668032 | 2 |
| C22×#13083562 | 2 |
| #19152169 | 2 |
| #19152165 | 2 |
| #19151989 | 2 |
| #19151986 | 2 |
| #19151981 | 2 |
| #19151969 | 2 |
| #19151556 | 2 |
| C2×AGL(1,ℤ/8)×C89 | 2 |
| #3154 | 89 |