Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 113 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. #31774711 | C2 | semidirect |
| 2. #31774710 | C2 | semidirect |
| 3. #31774340 | C2 | semidirect |
| 4. #31774339 | C2 | semidirect |
| 5. #31774336 | C2 | semidirect |
| 6. #31774328 | C2 | semidirect |
| 7. #31774327 | C2 | semidirect |
| 8. C2×#22576106 | C2 | semidirect |
| 9. Q32×D271 | C2 | semidirect |
| 10. #31774315 | C2 | semidirect |
| 11. #510×C271 | C2 | semidirect |
| 123. C271 | #3417 | semidirect |
| 130. #510 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774711 | 2 |
| #31774710 | 2 |
| #31774340 | 2 |
| #31774339 | 2 |
| #31774336 | 2 |
| #31774328 | 2 |
| #31774327 | 2 |
| C2×#22576106 | 2 |
| Q32×D271 | 2 |
| #31774315 | 2 |
| #510×C271 | 2 |
| #3417 | 271 |