Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
504 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 504 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×#22576188 | C2 | semidirect |
| 2. #31774475 | C2 | semidirect |
| 3. #31774461 | C2 | semidirect |
| 4. #31774150 | C2 | semidirect |
| 5. #31774143 | C2 | semidirect |
| 6. #31774133 | C2 | semidirect |
| 7. #31774126 | C2 | semidirect |
| 8. #31773939 | C2 | semidirect |
| 9. #31773894 | C2 | semidirect |
| 10. C2×#22576082 | C2 | semidirect |
| 11. C2×#131×C271 | C2 | semidirect |
| 19. #22576139 | C22 | semidirect |
| 23. #22576134 | C22 | semidirect |
| 29. #22576094 | C22 | semidirect |
| 30. #22576092 | C22 | semidirect |
| 31. #22576085 | C22 | semidirect |
| 32. #22576085 | C22 | semidirect |
| 35. #22576082 | C22 | semidirect |
| 36. #22576082 | C22 | semidirect |
| 40. C2×M16×C271 | C22 | semidirect |
| 42. C22×C8×C271 | C22 | semidirect |
| 79. M16×C271 | D4 | semidirect |
| 151. C271 | #3062 | semidirect |
| 154. C2×#131 | D271 | semidirect |
| 172. C2×M16 | C2×D271 | semidirect |
| 174. C22×C8 | C2×D271 | semidirect |
| 220. M16 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576188 | 2 |
| #31774475 | 2 |
| #31774461 | 2 |
| #31774150 | 2 |
| #31774143 | 2 |
| #31774133 | 2 |
| #31774126 | 2 |
| #31773939 | 2 |
| #31773894 | 2 |
| C2×#22576082 | 2 |
| C2×#131×C271 | 2 |
| #3062 | 271 |