Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#16864639 | C2 | semidirect |
| 2. #31774461 | C2 | semidirect |
| 3. #31774372 | C2 | semidirect |
| 4. #31774114 | C2 | semidirect |
| 5. #31774090 | C2 | semidirect |
| 6. #31773925 | C2 | semidirect |
| 7. #31773903 | C2 | semidirect |
| 8. #31773893 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C271 | C2 | semidirect |
| 14. #22576156 | C22 | semidirect |
| 15. #22576149 | C22 | semidirect |
| 19. D4×Dic271 | C22 | semidirect |
| 23. Dic271⋊C8 | C22 | semidirect |
| 24. #22576084 | C22 | semidirect |
| 25. #22576082 | C22 | semidirect |
| 26. #22576081 | C22 | semidirect |
| 30. C2×SD16×C271 | C22 | semidirect |
| 31. C2×D8×C271 | C22 | semidirect |
| 58. C2×D4×C271 | D4 | semidirect |
| 121. C271 | #3041 | semidirect |
| 123. C2×AGL(1,ℤ/8) | D271 | semidirect |
| 136. C2×SD16 | C2×D271 | semidirect |
| 139. C2×D8 | C2×D271 | semidirect |
| 168. C2×D4 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864639 | 2 |
| #31774461 | 2 |
| #31774372 | 2 |
| #31774114 | 2 |
| #31774090 | 2 |
| #31773925 | 2 |
| #31773903 | 2 |
| #31773893 | 2 |
| C2×AGL(1,ℤ/8)×C271 | 2 |
| #3041 | 271 |