Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
336 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. C2×#22579790 | C2 | semidirect |
| 5. C2×C8×Dic277 | C2 | semidirect |
| 6. #31799757 | C2 | semidirect |
| 7. #336×C277 | C2 | semidirect |
| 16. #22579792 | C4 | semidirect |
| 17. #22579792 | C4 | semidirect |
| 104. C277 | #1750 | semidirect |
| 112. #336 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22579837 | 2 |
| C2×#22579792 | 2 |
| C2×#22579790 | 2 |
| C2×C8×Dic277 | 2 |
| #31799757 | 2 |
| #336×C277 | 2 |
| #1750 | 277 |