Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
740 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 205 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×C4×D1108 | C2 | semidirect |
| 3. #31799905 | C2 | semidirect |
| 4. #31799903 | C2 | semidirect |
| 5. #31799881 | C2 | semidirect |
| 6. #31799878 | C2 | semidirect |
| 7. #31799867 | C2 | semidirect |
| 8. #31799848 | C2 | semidirect |
| 9. C2×C4×D4×C277 | C2 | semidirect |
| 13. #22579876 | C4 | semidirect |
| 33. C2×D1108 | C2×C4 | semidirect |
| 36. C2×C22⋊D277 | C2×C4 | semidirect |
| 47. C4×Dic277 | C2×C4 | semidirect |
| 51. C2×D4×C277 | C2×C4 | semidirect |
| 60. C42×C277 | D4 | semidirect |
| 123. C277 | #2328 | semidirect |
| 127. C2×C4×D4 | D277 | semidirect |
| 164. C2×D4 | C4×D277 | semidirect |
| 184. C42 | C22⋊D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22579876 | 2 |
| C2×C4×D1108 | 2 |
| #31799905 | 2 |
| #31799903 | 2 |
| #31799881 | 2 |
| #31799878 | 2 |
| #31799867 | 2 |
| #31799848 | 2 |
| C2×C4×D4×C277 | 2 |
| #2328 | 277 |