Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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. #26041907 | C2 | semidirect |
| 2. #26041643 | C2 | semidirect |
| 3. #26041638 | C2 | semidirect |
| 4. #26041633 | C2 | semidirect |
| 5. #26041625 | C2 | semidirect |
| 6. #26041284 | C2 | semidirect |
| 7. #26041280 | C2 | semidirect |
| 8. #26041275 | C2 | semidirect |
| 9. C2×#19153737 | C2 | semidirect |
| 10. #26041235 | C2 | semidirect |
| 14. #19153816 | C22 | semidirect |
| 16. #19153808 | C22 | semidirect |
| 21. #19153740 | C22 | semidirect |
| 22. #19153740 | C22 | semidirect |
| 23. #19153740 | C22 | semidirect |
| 28. #19153737 | C22 | semidirect |
| 29. #19153737 | C22 | semidirect |
| 30. #19153737 | C22 | semidirect |
| 31. #19153727 | C22 | semidirect |
| 32. C4×#13089678 | C22 | semidirect |
| 135. C181 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041907 | 2 |
| #26041643 | 2 |
| #26041638 | 2 |
| #26041633 | 2 |
| #26041625 | 2 |
| #26041284 | 2 |
| #26041280 | 2 |
| #26041275 | 2 |
| C2×#19153737 | 2 |
| #26041235 | 2 |
| #535×C181 | 2 |
| #3136 | 181 |