Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
652 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 209 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×#22579845 | C2 | semidirect |
| 4. #31799907 | C2 | semidirect |
| 6. #31799891 | C2 | semidirect |
| 7. #31799849 | C2 | semidirect |
| 8. C42×Dic277 | C2 | semidirect |
| 9. #382×C277 | C2 | semidirect |
| 13. #22579868 | C4 | semidirect |
| 33. C2×Dic554 | C2×C4 | semidirect |
| 46. #17984540 | C2×C4 | semidirect |
| 58. C42×C277 | C2×C4 | semidirect |
| 105. Dic277 | #124 | semidirect |
| 112. C277 | C4×#124 | semidirect |
| 120. #382 | D277 | semidirect |
| 171. C42 | C4×D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22579868 | 2 |
| C2×#22579845 | 2 |
| C2×#22579842 | 2 |
| #31799907 | 2 |
| #31799903 | 2 |
| #31799891 | 2 |
| #31799849 | 2 |
| C42×Dic277 | 2 |
| #382×C277 | 2 |
| C4×#124 | 277 |