Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 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. #26041834 | C2 | semidirect |
| 3. #26041642 | C2 | semidirect |
| 4. #26041627 | C2 | semidirect |
| 5. #26041626 | C2 | semidirect |
| 6. #26041625 | C2 | semidirect |
| 7. #26041282 | C2 | semidirect |
| 8. C4×#15668432 | C2 | semidirect |
| 9. #486×C181 | C2 | semidirect |
| 14. #19153816 | C22 | semidirect |
| 19. #19153807 | C22 | semidirect |
| 26. #19153738 | C22 | semidirect |
| 27. #19153737 | C22 | semidirect |
| 28. #19153736 | C22 | semidirect |
| 29. #19153726 | C22 | semidirect |
| 30. C4×#13089678 | C22 | semidirect |
| 31. C4⋊Q8×C181 | C22 | semidirect |
| 33. #102×C181 | C22 | semidirect |
| 34. C4×C8×C181 | C22 | semidirect |
| 123. C181 | #3138 | semidirect |
| 131. #486 | D181 | semidirect |
| 139. C4⋊Q8 | C2×D181 | semidirect |
| 155. #102 | C2×D181 | semidirect |
| 158. C4×C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041834 | 2 |
| #127×D181 | 2 |
| #26041642 | 2 |
| #26041627 | 2 |
| #26041626 | 2 |
| #26041625 | 2 |
| #26041282 | 2 |
| C4×#15668432 | 2 |
| #486×C181 | 2 |
| #3138 | 181 |