Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22576186 | C2 | semidirect |
| 2. C2×#22576167 | C2 | semidirect |
| 3. #31774475 | C2 | semidirect |
| 4. #31774148 | C2 | semidirect |
| 5. #31774141 | C2 | semidirect |
| 6. #31774131 | C2 | semidirect |
| 7. #31774124 | C2 | semidirect |
| 8. #31773940 | C2 | semidirect |
| 9. #31773891 | C2 | semidirect |
| 10. C2×#22576081 | C2 | semidirect |
| 11. #535×C271 | C2 | semidirect |
| 18. C2×#16864638 | C22 | semidirect |
| 20. C22×C271⋊C8 | C22 | semidirect |
| 21. #22576139 | C22 | semidirect |
| 23. #22576134 | C22 | semidirect |
| 27. #22576093 | C22 | semidirect |
| 28. #22576091 | C22 | semidirect |
| 29. #22576083 | C22 | semidirect |
| 30. #22576083 | C22 | semidirect |
| 33. #22576080 | C22 | semidirect |
| 34. #22576080 | C22 | semidirect |
| 54. #16864638 | D4 | semidirect |
| 151. C271 | #3062 | semidirect |
| 156. #535 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576186 | 2 |
| C2×#22576167 | 2 |
| #31774475 | 2 |
| #31774148 | 2 |
| #31774141 | 2 |
| #31774131 | 2 |
| #31774124 | 2 |
| #31773940 | 2 |
| #31773891 | 2 |
| C2×#22576081 | 2 |
| #535×C271 | 2 |
| #3062 | 271 |