Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 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. #26041762 | C2 | semidirect |
| 2. #26041600 | C2 | semidirect |
| 3. #26041600 | C2 | semidirect |
| 4. #26041595 | C2 | semidirect |
| 5. #26041590 | C2 | semidirect |
| 6. #26041322 | C2 | semidirect |
| 7. #26041315 | C2 | semidirect |
| 8. #26041284 | C2 | semidirect |
| 9. C2×#19153737 | C2 | semidirect |
| 10. #26041246 | C2 | semidirect |
| 18. #19153775 | C22 | semidirect |
| 20. C2×C4⋊Dic181 | C22 | semidirect |
| 21. #19153749 | C22 | semidirect |
| 22. #19153749 | C22 | semidirect |
| 23. #19153749 | C22 | semidirect |
| 24. #19153747 | C22 | semidirect |
| 25. #19153747 | C22 | semidirect |
| 26. #19153747 | C22 | semidirect |
| 31. C22⋊#13089678 | C22 | semidirect |
| 32. C22⋊#13089678 | C22 | semidirect |
| 134. C181 | #3096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041762 | 2 |
| #26041600 | 2 |
| #26041595 | 2 |
| #26041590 | 2 |
| #26041322 | 2 |
| #26041315 | 2 |
| #26041284 | 2 |
| C2×#19153737 | 2 |
| #26041246 | 2 |
| #535×C181 | 2 |
| #3096 | 181 |