Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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×#22576193 | C2 | semidirect |
| 3. #31774468 | C2 | semidirect |
| 4. #31774378 | C2 | semidirect |
| 5. #31774118 | C2 | semidirect |
| 6. #31774111 | C2 | semidirect |
| 7. #31774106 | C2 | semidirect |
| 8. #31774101 | C2 | semidirect |
| 9. #31773925 | C2 | semidirect |
| 10. C2×#22576083 | C2 | semidirect |
| 11. #417×C271 | C2 | semidirect |
| 146. C271 | #3046 | semidirect |
| 157. #417 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576193 | 2 |
| C2×#22576180 | 2 |
| #31774468 | 2 |
| #31774378 | 2 |
| #31774118 | 2 |
| #31774111 | 2 |
| #31774106 | 2 |
| #31774101 | 2 |
| #31773925 | 2 |
| C2×#22576083 | 2 |
| #417×C271 | 2 |
| #3046 | 271 |