Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 572 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×#15668043 | C2 | semidirect |
| 2. C2×#15668038 | C2 | semidirect |
| 3. #19152148 | C2 | semidirect |
| 4. #19151993 | C2 | semidirect |
| 5. #19151988 | C2 | semidirect |
| 6. #19151980 | C2 | semidirect |
| 7. C4×#13083558 | C2 | semidirect |
| 8. C2×#124×C89 | C2 | semidirect |
| 12. C2×#13083564 | C22 | semidirect |
| 14. C2×#13083561 | C22 | semidirect |
| 17. #15668012 | C22 | semidirect |
| 18. #15668009 | C22 | semidirect |
| 19. #15668000 | C22 | semidirect |
| 22. #15667923 | C22 | semidirect |
| 23. C4×#10623494 | C22 | semidirect |
| 42. #13083558 | D4 | semidirect |
| 107. C89 | #3153 | semidirect |
| 111. C2×#124 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668043 | 2 |
| C2×#15668038 | 2 |
| #19152148 | 2 |
| #19151993 | 2 |
| #19151988 | 2 |
| #19151980 | 2 |
| C4×#13083558 | 2 |
| C2×#124×C89 | 2 |
| #3153 | 89 |