Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
524 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 127 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×D8×D181 | C2 | semidirect |
| 2. C2×#19153822 | C2 | semidirect |
| 3. #26041845 | C2 | semidirect |
| 4. #26041531 | C2 | semidirect |
| 5. #26041530 | C2 | semidirect |
| 6. #26041516 | C2 | semidirect |
| 7. #26041515 | C2 | semidirect |
| 8. #26041512 | C2 | semidirect |
| 9. #26041316 | C2 | semidirect |
| 10. #26041282 | C2 | semidirect |
| 11. #466×C181 | C2 | semidirect |
| 18. C2×#15668433 | C22 | semidirect |
| 20. C2×#15668432 | C22 | semidirect |
| 22. C2×C8×D181 | C22 | semidirect |
| 25. #19153791 | C22 | semidirect |
| 26. #19153790 | C22 | semidirect |
| 27. #19153787 | C22 | semidirect |
| 31. #19153750 | C22 | semidirect |
| 32. #19153747 | C22 | semidirect |
| 33. #19153738 | C22 | semidirect |
| 34. #19153737 | C22 | semidirect |
| 35. #19153736 | C22 | semidirect |
| 37. C22×C8×C181 | C22 | semidirect |
| 38. #121×C181 | C22 | semidirect |
| 39. #107×C181 | C22 | semidirect |
| 40. #102×C181 | C22 | semidirect |
| 65. C8×D181 | D4 | semidirect |
| 150. C181 | #3058 | semidirect |
| 160. #466 | D181 | semidirect |
| 175. C22×C8 | C2×D181 | semidirect |
| 181. #121 | C2×D181 | semidirect |
| 186. #107 | C2×D181 | semidirect |
| 191. #102 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D181 | 2 |
| C2×#19153822 | 2 |
| #26041845 | 2 |
| #26041531 | 2 |
| #26041530 | 2 |
| #26041516 | 2 |
| #26041515 | 2 |
| #26041512 | 2 |
| #26041316 | 2 |
| #26041282 | 2 |
| #466×C181 | 2 |
| #3058 | 181 |