Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 125 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×#15668009 | C2 | semidirect |
| 2. #19151988 | C2 | semidirect |
| 3. #19151964 | C2 | semidirect |
| 4. #19151798 | C2 | semidirect |
| 5. #19151793 | C2 | semidirect |
| 6. #19151748 | C2 | semidirect |
| 7. #19151731 | C2 | semidirect |
| 8. #19151655 | C2 | semidirect |
| 9. #529×C89 | C2 | semidirect |
| 13. C2×#13083561 | C22 | semidirect |
| 14. C2×#13083559 | C22 | semidirect |
| 19. C4⋊#10623494 | C22 | semidirect |
| 20. #15667932 | C22 | semidirect |
| 21. #15667932 | C22 | semidirect |
| 23. #15667923 | C22 | semidirect |
| 25. #125×C89 | C22 | semidirect |
| 26. #124×C89 | C22 | semidirect |
| 30. C4×Q8×C89 | C22 | semidirect |
| 32. C4×D4×C89 | C22 | semidirect |
| 128. C89 | #3217 | semidirect |
| 130. #529 | D89 | semidirect |
| 148. #125 | C2×D89 | semidirect |
| 149. #124 | C2×D89 | semidirect |
| 153. C4×Q8 | C2×D89 | semidirect |
| 155. C4×D4 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668009 | 2 |
| #19151988 | 2 |
| #19151964 | 2 |
| #19151798 | 2 |
| #19151793 | 2 |
| #19151748 | 2 |
| #19151731 | 2 |
| #19151655 | 2 |
| #529×C89 | 2 |
| #3217 | 89 |