Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31774450 | C2 | semidirect |
| 3. #31774264 | C2 | semidirect |
| 4. #31774260 | C2 | semidirect |
| 5. #31774258 | C2 | semidirect |
| 6. #31774255 | C2 | semidirect |
| 7. #31773894 | C2 | semidirect |
| 8. #31773893 | C2 | semidirect |
| 9. #31773891 | C2 | semidirect |
| 10. C2×#22576070 | C2 | semidirect |
| 11. #416×C271 | C2 | semidirect |
| 125. C271 | #3135 | semidirect |
| 136. #416 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774450 | 2 |
| #31774443 | 2 |
| #31774264 | 2 |
| #31774260 | 2 |
| #31774258 | 2 |
| #31774255 | 2 |
| #31773894 | 2 |
| #31773893 | 2 |
| #31773891 | 2 |
| C2×#22576070 | 2 |
| #416×C271 | 2 |
| #3135 | 271 |