Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19153842 | C2 | semidirect |
| 2. C2×#19153822 | C2 | semidirect |
| 3. #26041860 | C2 | semidirect |
| 4. #26041846 | C2 | semidirect |
| 5. #26041531 | C2 | semidirect |
| 6. #26041524 | C2 | semidirect |
| 7. #26041514 | C2 | semidirect |
| 8. #26041507 | C2 | semidirect |
| 9. #26041319 | C2 | semidirect |
| 10. #26041276 | C2 | semidirect |
| 11. C2×#102×C181 | C2 | semidirect |
| 19. C2×#15668432 | C22 | semidirect |
| 20. C2×C8×D181 | C22 | semidirect |
| 24. #19153796 | C22 | semidirect |
| 26. #19153791 | C22 | semidirect |
| 32. #19153749 | C22 | semidirect |
| 33. #19153747 | C22 | semidirect |
| 34. #19153741 | C22 | semidirect |
| 35. #19153741 | C22 | semidirect |
| 36. #19153738 | C22 | semidirect |
| 37. #19153738 | C22 | semidirect |
| 60. #15668433 | D4 | semidirect |
| 151. C181 | #3062 | semidirect |
| 163. C2×#102 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153842 | 2 |
| C2×#19153822 | 2 |
| #26041860 | 2 |
| #26041846 | 2 |
| #26041531 | 2 |
| #26041524 | 2 |
| #26041514 | 2 |
| #26041507 | 2 |
| #26041319 | 2 |
| #26041276 | 2 |
| C2×#102×C181 | 2 |
| #3062 | 181 |