Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31774502 | C2 | semidirect |
| 2. #31774221 | C2 | semidirect |
| 3. #31774197 | C2 | semidirect |
| 4. #31774092 | C2 | semidirect |
| 5. #31774031 | C2 | semidirect |
| 6. #31774007 | C2 | semidirect |
| 7. C4×#16864639 | C2 | semidirect |
| 8. #31773958 | C2 | semidirect |
| 9. #518×C271 | C2 | semidirect |
| 12. #22576157 | C22 | semidirect |
| 13. #22576152 | C22 | semidirect |
| 17. C4×D1084 | C22 | semidirect |
| 18. #22576093 | C22 | semidirect |
| 19. #22576091 | C22 | semidirect |
| 20. C4⋊(C271⋊C8) | C22 | semidirect |
| 23. #22576080 | C22 | semidirect |
| 24. #22576080 | C22 | semidirect |
| 26. #22576071 | C22 | semidirect |
| 27. C4×C271⋊C8 | C22 | semidirect |
| 108. C271 | #3122 | semidirect |
| 111. #518 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774502 | 2 |
| #31774221 | 2 |
| #31774197 | 2 |
| #31774092 | 2 |
| #31774031 | 2 |
| #31774007 | 2 |
| C4×#16864639 | 2 |
| #31773958 | 2 |
| #518×C271 | 2 |
| #3122 | 271 |