Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
450 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 129 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. #31774431 | C2 | semidirect |
| 2. #31774227 | C2 | semidirect |
| 3. #31774210 | C2 | semidirect |
| 4. #31774197 | C2 | semidirect |
| 5. #31774112 | C2 | semidirect |
| 6. #31774048 | C2 | semidirect |
| 8. #31774007 | C2 | semidirect |
| 9. #31773997 | C2 | semidirect |
| 10. #31773954 | C2 | semidirect |
| 11. C2×C4×D4×C271 | C2 | semidirect |
| 15. #22576152 | C22 | semidirect |
| 16. #22576148 | C22 | semidirect |
| 20. C4×Dic542 | C22 | semidirect |
| 21. C4×D1084 | C22 | semidirect |
| 24. #22576093 | C22 | semidirect |
| 25. #22576091 | C22 | semidirect |
| 26. C4⋊(C271⋊C8) | C22 | semidirect |
| 27. #22576083 | C22 | semidirect |
| 30. #22576080 | C22 | semidirect |
| 33. #22576071 | C22 | semidirect |
| 140. C271 | #3114 | semidirect |
| 143. C2×C4×D4 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774431 | 2 |
| #31774227 | 2 |
| #31774210 | 2 |
| #31774197 | 2 |
| #31774112 | 2 |
| #31774048 | 2 |
| #31774031 | 2 |
| #31774007 | 2 |
| #31773997 | 2 |
| #31773954 | 2 |
| C2×C4×D4×C271 | 2 |
| #3114 | 271 |