Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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. C2×#22576188 | C2 | semidirect |
| 2. C22×D2168 | C2 | semidirect |
| 3. #31774466 | C2 | semidirect |
| 4. #31774371 | C2 | semidirect |
| 5. #31774113 | C2 | semidirect |
| 6. #31774093 | C2 | semidirect |
| 7. #31773903 | C2 | semidirect |
| 8. #31773894 | C2 | semidirect |
| 9. #424×C271 | C2 | semidirect |
| 14. C2×#16864643 | C22 | semidirect |
| 17. C2×D2168 | C22 | semidirect |
| 18. #22576157 | C22 | semidirect |
| 19. #22576148 | C22 | semidirect |
| 22. C4×D1084 | C22 | semidirect |
| 26. #22576085 | C22 | semidirect |
| 27. #22576082 | C22 | semidirect |
| 28. #22576082 | C22 | semidirect |
| 32. C4⋊C8×C271 | C22 | semidirect |
| 44. C2×D1084 | D4 | semidirect |
| 121. C271 | #3041 | semidirect |
| 129. #424 | D271 | semidirect |
| 151. C4⋊C8 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576188 | 2 |
| C22×D2168 | 2 |
| #31774466 | 2 |
| #31774371 | 2 |
| #31774113 | 2 |
| #31774093 | 2 |
| #31773903 | 2 |
| #31773894 | 2 |
| #424×C271 | 2 |
| #3041 | 271 |