Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
488 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 488 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. #26041653 | C2 | semidirect |
| 4. #26041626 | C2 | semidirect |
| 5. #26041625 | C2 | semidirect |
| 6. #26041477 | C2 | semidirect |
| 7. #26041428 | C2 | semidirect |
| 8. #26041330 | C2 | semidirect |
| 9. #492×C181 | C2 | semidirect |
| 13. C2×#15668436 | C22 | semidirect |
| 14. #19153816 | C22 | semidirect |
| 22. Q8×Dic181 | C22 | semidirect |
| 26. #19153745 | C22 | semidirect |
| 27. #19153738 | C22 | semidirect |
| 28. #19153737 | C22 | semidirect |
| 30. C4×#13089678 | C22 | semidirect |
| 31. C2×SD16×C181 | C22 | semidirect |
| 32. C4⋊Q8×C181 | C22 | semidirect |
| 34. C4×C8×C181 | C22 | semidirect |
| 87. C4×D181 | SD16 | semidirect |
| 124. C181 | #3208 | semidirect |
| 129. #492 | D181 | semidirect |
| 139. C2×SD16 | C2×D181 | semidirect |
| 141. C4⋊Q8 | C2×D181 | semidirect |
| 159. 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 |
| #26041653 | 2 |
| #26041626 | 2 |
| #26041625 | 2 |
| #26041477 | 2 |
| #26041428 | 2 |
| #26041330 | 2 |
| #492×C181 | 2 |
| #3208 | 181 |