Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #31774525 | C2 | semidirect |
| 3. #31774198 | C2 | semidirect |
| 4. #31774198 | C2 | semidirect |
| 5. #31774188 | C2 | semidirect |
| 6. #31774178 | C2 | semidirect |
| 7. #31773939 | C2 | semidirect |
| 8. #31773935 | C2 | semidirect |
| 11. #424×C271 | C2 | semidirect |
| 13. #22576160 | C22 | semidirect |
| 15. #22576152 | C22 | semidirect |
| 26. #22576094 | C22 | semidirect |
| 27. #22576094 | C22 | semidirect |
| 28. #22576094 | C22 | semidirect |
| 29. #22576092 | C22 | semidirect |
| 30. #22576092 | C22 | semidirect |
| 31. #22576092 | C22 | semidirect |
| 39. C4⋊C8×C271 | C22 | semidirect |
| 40. C4⋊C8×C271 | C22 | semidirect |
| 45. C2×D1084 | Q8 | semidirect |
| 124. C271 | #3081 | semidirect |
| 134. #424 | D271 | semidirect |
| 160. C4⋊C8 | C2×D271 | semidirect |
| 161. C4⋊C8 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774525 | 2 |
| #31774371 | 2 |
| #31774198 | 2 |
| #31774188 | 2 |
| #31774178 | 2 |
| #31773939 | 2 |
| #31773935 | 2 |
| #31773903 | 2 |
| C2×#22576082 | 2 |
| #424×C271 | 2 |
| #3081 | 271 |