Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 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. #31774711 | C2 | semidirect |
| 2. #31774708 | C2 | semidirect |
| 3. #31774280 | C2 | semidirect |
| 4. #31774172 | C2 | semidirect |
| 5. #31774164 | C2 | semidirect |
| 6. #31774158 | C2 | semidirect |
| 7. #31774075 | C2 | semidirect |
| 8. #31774068 | C2 | semidirect |
| 9. #31774014 | C2 | semidirect |
| 10. #31774012 | C2 | semidirect |
| 11. #576×C271 | C2 | semidirect |
| 12. #22576207 | C22 | semidirect |
| 15. #22576190 | C22 | semidirect |
| 18. #22576186 | C22 | semidirect |
| 22. C2×Dic1084 | C22 | semidirect |
| 25. C2×#16864642 | C22 | semidirect |
| 26. #22576167 | C22 | semidirect |
| 27. #22576166 | C22 | semidirect |
| 28. #22576147 | C22 | semidirect |
| 29. #22576096 | C22 | semidirect |
| 30. #22576095 | C22 | semidirect |
| 32. #22576087 | C22 | semidirect |
| 33. #22576086 | C22 | semidirect |
| 34. #22576078 | C22 | semidirect |
| 35. #22576077 | C22 | semidirect |
| 36. C8×Dic271 | C22 | semidirect |
| 149. C271 | #3290 | semidirect |
| 153. #576 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774711 | 2 |
| #31774708 | 2 |
| #31774280 | 2 |
| #31774172 | 2 |
| #31774164 | 2 |
| #31774158 | 2 |
| #31774075 | 2 |
| #31774068 | 2 |
| #31774014 | 2 |
| #31774012 | 2 |
| #576×C271 | 2 |
| #3290 | 271 |