Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22576205 | C2 | semidirect |
| 2. C2×#22576188 | C2 | semidirect |
| 3. C22×#16864639 | C2 | semidirect |
| 4. #31774466 | C2 | semidirect |
| 5. #31774043 | C2 | semidirect |
| 6. #31774032 | C2 | semidirect |
| 7. #31773891 | C2 | semidirect |
| 8. #31773865 | C2 | semidirect |
| 9. #418×C271 | C2 | semidirect |
| 15. C2×#16864653 | C22 | semidirect |
| 16. C22×D1084 | C22 | semidirect |
| 19. C2×D4×D271 | C22 | semidirect |
| 21. C2×#16864643 | C22 | semidirect |
| 22. C2×D2168 | C22 | semidirect |
| 24. C2×#16864639 | C22 | semidirect |
| 25. C22×C271⋊C8 | C22 | semidirect |
| 28. #22576135 | C22 | semidirect |
| 30. #22576083 | C22 | semidirect |
| 31. #22576080 | C22 | semidirect |
| 32. (C2×D271)⋊C8 | C22 | semidirect |
| 34. C2×M16×C271 | C22 | semidirect |
| 35. #117×C271 | C22 | semidirect |
| 36. #102×C271 | C22 | semidirect |
| 42. #16864654 | D4 | semidirect |
| 75. C2×D4×C271 | D4 | semidirect |
| 151. C271 | #3008 | semidirect |
| 159. #418 | D271 | semidirect |
| 178. C2×M16 | C2×D271 | semidirect |
| 184. #117 | C2×D271 | semidirect |
| 187. #102 | C2×D271 | semidirect |
| 218. C2×D4 | D1084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576205 | 2 |
| C2×#22576188 | 2 |
| C22×#16864639 | 2 |
| #31774466 | 2 |
| #31774043 | 2 |
| #31774032 | 2 |
| #31773891 | 2 |
| #31773865 | 2 |
| #418×C271 | 2 |
| #3008 | 271 |