Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
740 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 2. C2×D4×Dic271 | C2 | semidirect |
| 3. C2×#22576122 | C2 | semidirect |
| 4. #31773799 | C2 | semidirect |
| 5. #31773774 | C2 | semidirect |
| 6. #31773773 | C2 | semidirect |
| 7. #31773762 | C2 | semidirect |
| 8. #31773743 | C2 | semidirect |
| 9. #390×C271 | C2 | semidirect |
| 14. #22576156 | C4 | semidirect |
| 33. C2×D1084 | C2×C4 | semidirect |
| 36. C2×C22⋊D271 | C2×C4 | semidirect |
| 49. C4×Dic271 | C2×C4 | semidirect |
| 50. C4×Dic271 | D4 | semidirect |
| 54. C2×D4×C271 | C2×C4 | semidirect |
| 123. C271 | #2328 | semidirect |
| 129. #390 | D271 | semidirect |
| 164. C2×D4 | C4×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576156 | 2 |
| C2×D4×Dic271 | 2 |
| C2×#22576122 | 2 |
| #31773799 | 2 |
| #31773774 | 2 |
| #31773773 | 2 |
| #31773762 | 2 |
| #31773743 | 2 |
| #390×C271 | 2 |
| #2328 | 271 |