Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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×#15668038 | C2 | semidirect |
| 2. #19152148 | C2 | semidirect |
| 3. #19151985 | C2 | semidirect |
| 4. #19151974 | C2 | semidirect |
| 5. #19151970 | C2 | semidirect |
| 6. C4×#13083558 | C2 | semidirect |
| 7. C2×#127×C89 | C2 | semidirect |
| 10. C2×#13083562 | C22 | semidirect |
| 11. C2×#13083559 | C22 | semidirect |
| 13. #15668012 | C22 | semidirect |
| 14. #15668009 | C22 | semidirect |
| 15. #15668000 | C22 | semidirect |
| 18. #15667923 | C22 | semidirect |
| 19. C4×#10623494 | C22 | semidirect |
| 34. #13083558 | D4 | semidirect |
| 71. #10623494 | C2×D4 | semidirect |
| 82. C4×C89 | AGL(1,ℤ/8) | semidirect |
| 91. C89 | #3151 | semidirect |
| 94. C2×#127 | D89 | semidirect |
| 174. C4 | #15668038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668038 | 2 |
| #19152148 | 2 |
| #19151985 | 2 |
| #19151974 | 2 |
| #19151970 | 2 |
| C4×#13083558 | 2 |
| C2×#127×C89 | 2 |
| #3151 | 89 |