Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 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×#22576193 | C2 | semidirect |
| 3. C2×#22576147 | C2 | semidirect |
| 4. #31774365 | C2 | semidirect |
| 5. #31774118 | C2 | semidirect |
| 6. #31774111 | C2 | semidirect |
| 7. #31773920 | C2 | semidirect |
| 8. #31773905 | C2 | semidirect |
| 9. #418×C271 | C2 | semidirect |
| 14. C2×Dic1084 | C22 | semidirect |
| 15. C2×#16864643 | C22 | semidirect |
| 22. #22576125 | C22 | semidirect |
| 23. #22576122 | C22 | semidirect |
| 29. Dic271⋊C8 | C22 | semidirect |
| 30. #22576083 | C22 | semidirect |
| 125. C271 | #3040 | semidirect |
| 135. #418 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576193 | 2 |
| C2×#22576186 | 2 |
| C2×#22576147 | 2 |
| #31774365 | 2 |
| #31774118 | 2 |
| #31774111 | 2 |
| #31773920 | 2 |
| #31773905 | 2 |
| #418×C271 | 2 |
| #3040 | 271 |