Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#22576186 | C2 | semidirect |
| 2. C2×#22576166 | C2 | semidirect |
| 3. #31774478 | C2 | semidirect |
| 4. #31774464 | C2 | semidirect |
| 5. #31774149 | C2 | semidirect |
| 6. #31774142 | C2 | semidirect |
| 7. #31774132 | C2 | semidirect |
| 8. #31774125 | C2 | semidirect |
| 9. #31773937 | C2 | semidirect |
| 10. #31773894 | C2 | semidirect |
| 11. C2×#102×C271 | C2 | semidirect |
| 19. C2×#16864637 | C22 | semidirect |
| 20. C2×C8×D271 | C22 | semidirect |
| 24. #22576140 | C22 | semidirect |
| 26. #22576135 | C22 | semidirect |
| 32. #22576093 | C22 | semidirect |
| 33. #22576091 | C22 | semidirect |
| 34. #22576085 | C22 | semidirect |
| 35. #22576085 | C22 | semidirect |
| 36. #22576082 | C22 | semidirect |
| 37. #22576082 | C22 | semidirect |
| 60. #16864638 | D4 | semidirect |
| 151. C271 | #3062 | semidirect |
| 163. C2×#102 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576186 | 2 |
| C2×#22576166 | 2 |
| #31774478 | 2 |
| #31774464 | 2 |
| #31774149 | 2 |
| #31774142 | 2 |
| #31774132 | 2 |
| #31774125 | 2 |
| #31773937 | 2 |
| #31773894 | 2 |
| C2×#102×C271 | 2 |
| #3062 | 271 |