Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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. C2×#22576182 | C2 | semidirect |
| 3. #31774466 | C2 | semidirect |
| 4. #31774377 | C2 | semidirect |
| 5. #31774120 | C2 | semidirect |
| 6. #31774113 | C2 | semidirect |
| 7. #31774098 | C2 | semidirect |
| 8. #31774093 | C2 | semidirect |
| 9. #31773899 | C2 | semidirect |
| 10. C2×#22576082 | C2 | semidirect |
| 11. #424×C271 | C2 | semidirect |
| 17. C2×Dic1084 | C22 | semidirect |
| 19. C2×#16864643 | C22 | semidirect |
| 20. C2×#16864643 | C22 | semidirect |
| 22. C2×D2168 | C22 | semidirect |
| 28. C4×Dic542 | C22 | semidirect |
| 29. C4×D1084 | C22 | semidirect |
| 34. #22576085 | C22 | semidirect |
| 37. #22576082 | C22 | semidirect |
| 41. C4⋊C8×C271 | C22 | semidirect |
| 42. C4⋊C8×C271 | C22 | semidirect |
| 47. #16864654 | D4 | semidirect |
| 154. C271 | #3045 | semidirect |
| 164. #424 | D271 | semidirect |
| 192. C4⋊C8 | C2×D271 | semidirect |
| 193. 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 |
| C2×#22576182 | 2 |
| #31774466 | 2 |
| #31774377 | 2 |
| #31774120 | 2 |
| #31774113 | 2 |
| #31774098 | 2 |
| #31774093 | 2 |
| #31773899 | 2 |
| C2×#22576082 | 2 |
| #424×C271 | 2 |
| #3045 | 271 |