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×#19153824 | C2 | semidirect |
| 3. #26041845 | C2 | semidirect |
| 4. #26041533 | C2 | semidirect |
| 5. #26041532 | C2 | semidirect |
| 6. #26041529 | C2 | semidirect |
| 7. #26041514 | C2 | semidirect |
| 8. #26041513 | C2 | semidirect |
| 9. #26041314 | C2 | semidirect |
| 10. #26041282 | C2 | semidirect |
| 11. #469×C181 | C2 | semidirect |
| 19. C2×#15668432 | C22 | semidirect |
| 20. C22×#13089678 | C22 | semidirect |
| 22. C2×C8×D181 | C22 | semidirect |
| 25. #19153791 | C22 | semidirect |
| 26. #19153790 | C22 | semidirect |
| 27. #19153787 | C22 | semidirect |
| 31. #19153749 | C22 | semidirect |
| 32. #19153748 | C22 | semidirect |
| 33. #19153738 | C22 | semidirect |
| 34. #19153737 | C22 | semidirect |
| 35. #19153736 | C22 | semidirect |
| 37. C2×M16×C181 | C22 | semidirect |
| 38. #121×C181 | C22 | semidirect |
| 39. #106×C181 | C22 | semidirect |
| 40. #102×C181 | C22 | semidirect |
| 65. C8×D181 | D4 | semidirect |
| 146. C181 | #3058 | semidirect |
| 154. #469 | D181 | semidirect |
| 168. C2×M16 | C2×D181 | semidirect |
| 177. #121 | C2×D181 | semidirect |
| 183. #106 | C2×D181 | semidirect |
| 187. #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×#19153824 | 2 |
| #26041845 | 2 |
| #26041533 | 2 |
| #26041532 | 2 |
| #26041529 | 2 |
| #26041514 | 2 |
| #26041513 | 2 |
| #26041314 | 2 |
| #26041282 | 2 |
| #469×C181 | 2 |
| #3058 | 181 |