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×#22576206 | C2 | semidirect |
| 2. C22×#16864639 | C2 | semidirect |
| 3. #31774464 | C2 | semidirect |
| 4. #31774041 | C2 | semidirect |
| 5. #31774029 | C2 | semidirect |
| 6. #31773903 | C2 | semidirect |
| 7. #31773893 | C2 | semidirect |
| 8. #31773865 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C271 | C2 | semidirect |
| 12. C2×#16864655 | C22 | semidirect |
| 18. C2×D4×D271 | C22 | semidirect |
| 20. C2×#16864639 | C22 | semidirect |
| 21. C22×C271⋊C8 | C22 | semidirect |
| 24. #22576131 | C22 | semidirect |
| 26. #22576119 | C22 | semidirect |
| 27. #22576084 | C22 | semidirect |
| 28. #22576082 | C22 | semidirect |
| 29. #22576081 | C22 | semidirect |
| 30. (C2×D271)⋊C8 | C22 | semidirect |
| 32. C22×D4×C271 | C22 | semidirect |
| 34. C2×SD16×C271 | C22 | semidirect |
| 35. C2×D8×C271 | C22 | semidirect |
| 36. C2×M16×C271 | C22 | semidirect |
| 50. C2×D1084 | D4 | semidirect |
| 69. #41×C271 | D4 | semidirect |
| 151. C271 | #3008 | semidirect |
| 154. C2×AGL(1,ℤ/8) | D271 | semidirect |
| 172. C22×D4 | C2×D271 | semidirect |
| 174. C2×SD16 | C2×D271 | semidirect |
| 177. C2×D8 | C2×D271 | semidirect |
| 178. C2×M16 | C2×D271 | semidirect |
| 198. #41 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576206 | 2 |
| C22×#16864639 | 2 |
| #31774464 | 2 |
| #31774041 | 2 |
| #31774029 | 2 |
| #31773903 | 2 |
| #31773893 | 2 |
| #31773865 | 2 |
| C2×AGL(1,ℤ/8)×C271 | 2 |
| #3008 | 271 |