Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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. C2×#22576186 | C2 | semidirect |
| 2. C2×#22576182 | C2 | semidirect |
| 3. #31774464 | C2 | semidirect |
| 4. #31774378 | C2 | semidirect |
| 5. #31774118 | C2 | semidirect |
| 6. #31774111 | C2 | semidirect |
| 7. #31774096 | C2 | semidirect |
| 8. #31774091 | C2 | semidirect |
| 9. #31773923 | C2 | semidirect |
| 10. #31773896 | C2 | semidirect |
| 11. C2×#102×C271 | C2 | semidirect |
| 16. C2×Dic1084 | C22 | semidirect |
| 17. C2×#16864643 | C22 | semidirect |
| 18. C2×#16864643 | C22 | semidirect |
| 20. C2×D2168 | C22 | semidirect |
| 28. #22576125 | C22 | semidirect |
| 29. #22576122 | C22 | semidirect |
| 34. Dic271⋊C8 | C22 | semidirect |
| 35. Dic271⋊C8 | C22 | semidirect |
| 36. #22576083 | C22 | semidirect |
| 37. #22576080 | C22 | semidirect |
| 46. #16864654 | D4 | semidirect |
| 154. C271 | #3045 | semidirect |
| 166. C2×#102 | 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×#22576182 | 2 |
| #31774464 | 2 |
| #31774378 | 2 |
| #31774118 | 2 |
| #31774111 | 2 |
| #31774096 | 2 |
| #31774091 | 2 |
| #31773923 | 2 |
| #31773896 | 2 |
| C2×#102×C271 | 2 |
| #3045 | 271 |