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×#22576186 | C2 | semidirect |
| 3. #31774464 | C2 | semidirect |
| 4. #31774039 | C2 | semidirect |
| 5. #31774029 | C2 | semidirect |
| 6. #31773902 | C2 | semidirect |
| 7. #31773894 | C2 | semidirect |
| 8. #31773863 | C2 | semidirect |
| 9. C22×D8×C271 | C2 | semidirect |
| 15. C2×#16864653 | C22 | semidirect |
| 18. C2×D4×D271 | C22 | semidirect |
| 20. C2×#16864642 | C22 | semidirect |
| 21. C2×#16864639 | C22 | semidirect |
| 22. C2×#16864638 | C22 | semidirect |
| 25. #22576131 | C22 | semidirect |
| 27. #22576119 | C22 | semidirect |
| 28. #22576085 | C22 | semidirect |
| 29. #22576082 | C22 | semidirect |
| 30. #22576081 | C22 | semidirect |
| 31. (C2×D271)⋊C8 | C22 | semidirect |
| 33. C22×D4×C271 | C22 | semidirect |
| 35. C2×D8×C271 | C22 | semidirect |
| 36. C22×C8×C271 | C22 | semidirect |
| 41. #16864654 | D4 | semidirect |
| 76. C2×D4×C271 | D4 | semidirect |
| 151. C271 | #3008 | semidirect |
| 155. C22×D8 | D271 | semidirect |
| 172. C22×D4 | C2×D271 | semidirect |
| 177. C2×D8 | C2×D271 | semidirect |
| 179. C22×C8 | C2×D271 | semidirect |
| 217. C2×D4 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576205 | 2 |
| C2×#22576186 | 2 |
| #31774464 | 2 |
| #31774039 | 2 |
| #31774029 | 2 |
| #31773902 | 2 |
| #31773894 | 2 |
| #31773863 | 2 |
| C22×D8×C271 | 2 |
| #3008 | 271 |