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×#19153841 | C2 | semidirect |
| 2. C2×#19153822 | C2 | semidirect |
| 3. #26041857 | C2 | semidirect |
| 4. #26041848 | C2 | semidirect |
| 5. #26041531 | C2 | semidirect |
| 6. #26041528 | C2 | semidirect |
| 7. #26041514 | C2 | semidirect |
| 8. #26041511 | C2 | semidirect |
| 9. #26041322 | C2 | semidirect |
| 10. C2×#19153738 | C2 | semidirect |
| 11. #416×C181 | C2 | semidirect |
| 19. C2×#15668432 | C22 | semidirect |
| 20. C2×C8×D181 | C22 | semidirect |
| 24. #19153792 | C22 | semidirect |
| 29. #19153787 | C22 | semidirect |
| 32. #19153749 | C22 | semidirect |
| 33. #19153747 | C22 | semidirect |
| 39. #103×C181 | C22 | semidirect |
| 40. #103×C181 | C22 | semidirect |
| 41. #102×C181 | C22 | semidirect |
| 42. #102×C181 | C22 | semidirect |
| 60. #15668433 | D4 | semidirect |
| 151. C181 | #3062 | semidirect |
| 162. #416 | D181 | semidirect |
| 189. #103 | C2×D181 | semidirect |
| 190. #103 | C2×D181 | semidirect |
| 193. #102 | C2×D181 | semidirect |
| 194. #102 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153841 | 2 |
| C2×#19153822 | 2 |
| #26041857 | 2 |
| #26041848 | 2 |
| #26041531 | 2 |
| #26041528 | 2 |
| #26041514 | 2 |
| #26041511 | 2 |
| #26041322 | 2 |
| C2×#19153738 | 2 |
| #416×C181 | 2 |
| #3062 | 181 |