Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
488 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 129 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. #19152148 | C2 | semidirect |
| 2. C2×C4×D356 | C2 | semidirect |
| 3. #19151917 | C2 | semidirect |
| 4. #19151889 | C2 | semidirect |
| 5. #19151794 | C2 | semidirect |
| 6. #19151734 | C2 | semidirect |
| 7. #19151711 | C2 | semidirect |
| 8. #432×C89 | C2 | semidirect |
| 13. #15668012 | C22 | semidirect |
| 14. #15668009 | C22 | semidirect |
| 23. C4×D356 | C22 | semidirect |
| 26. #15667944 | C22 | semidirect |
| 28. #15667934 | C22 | semidirect |
| 30. C4⋊C8×C89 | C22 | semidirect |
| 32. #97×C89 | C22 | semidirect |
| 89. D356 | #41 | semidirect |
| 121. C89 | #3109 | semidirect |
| 129. #432 | D89 | semidirect |
| 149. C4⋊C8 | C2×D89 | semidirect |
| 153. #97 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152148 | 2 |
| C2×C4×D356 | 2 |
| #19151917 | 2 |
| #19151889 | 2 |
| #19151794 | 2 |
| #19151734 | 2 |
| #19151711 | 2 |
| #432×C89 | 2 |
| #3109 | 89 |