Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 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×#22576207 | C2 | semidirect |
| 2. C22×#16864642 | C2 | semidirect |
| 3. #31774464 | C2 | semidirect |
| 4. #31774039 | C2 | semidirect |
| 5. #31774034 | C2 | semidirect |
| 6. #31773907 | C2 | semidirect |
| 7. #31773893 | C2 | semidirect |
| 8. #31773865 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C271 | C2 | semidirect |
| 15. C2×#16864653 | C22 | semidirect |
| 18. C2×Q8×D271 | C22 | semidirect |
| 27. #22576085 | C22 | semidirect |
| 28. #22576084 | C22 | semidirect |
| 29. #22576081 | C22 | semidirect |
| 30. (C2×D271)⋊C8 | C22 | semidirect |
| 48. C2×Dic542 | D4 | semidirect |
| 69. #41×C271 | D4 | semidirect |
| 145. C271 | #3010 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D271 | semidirect |
| 191. #41 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576207 | 2 |
| C22×#16864642 | 2 |
| #31774464 | 2 |
| #31774039 | 2 |
| #31774034 | 2 |
| #31773907 | 2 |
| #31773893 | 2 |
| #31773865 | 2 |
| C2×AGL(1,ℤ/8)×C271 | 2 |
| #3010 | 271 |