Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 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. #31774431 | C2 | semidirect |
| 2. C2×C4×D1084 | C2 | semidirect |
| 3. #31774228 | C2 | semidirect |
| 4. #31774211 | C2 | semidirect |
| 5. #31774198 | C2 | semidirect |
| 6. #31774113 | C2 | semidirect |
| 7. #31774050 | C2 | semidirect |
| 9. #31774010 | C2 | semidirect |
| 10. #31773999 | C2 | semidirect |
| 11. #432×C271 | C2 | semidirect |
| 17. #22576152 | C22 | semidirect |
| 18. #22576148 | C22 | semidirect |
| 22. C4×Dic542 | C22 | semidirect |
| 27. C4×D1084 | C22 | semidirect |
| 32. #22576094 | C22 | semidirect |
| 33. #22576092 | C22 | semidirect |
| 34. #22576085 | C22 | semidirect |
| 37. #22576082 | C22 | semidirect |
| 39. C4⋊C8×C271 | C22 | semidirect |
| 42. #97×C271 | C22 | semidirect |
| 140. C271 | #3114 | semidirect |
| 152. #432 | D271 | semidirect |
| 176. C4⋊C8 | C2×D271 | semidirect |
| 183. #97 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774431 | 2 |
| C2×C4×D1084 | 2 |
| #31774228 | 2 |
| #31774211 | 2 |
| #31774198 | 2 |
| #31774113 | 2 |
| #31774050 | 2 |
| #31774033 | 2 |
| #31774010 | 2 |
| #31773999 | 2 |
| #432×C271 | 2 |
| #3114 | 271 |