Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 89 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. #31800019 | C2 | semidirect |
| 3. #31800008 | C2 | semidirect |
| 4. C2×#22579796 | C2 | semidirect |
| 5. #31799774 | C2 | semidirect |
| 6. #31799760 | C2 | semidirect |
| 7. #568×C277 | C2 | semidirect |
| 11. C2×#17984550 | C4 | semidirect |
| 12. C2×#17984548 | C4 | semidirect |
| 112. C277 | #1903 | semidirect |
| 115. #568 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22579905 | 2 |
| #31800019 | 2 |
| #31800008 | 2 |
| C2×#22579796 | 2 |
| #31799774 | 2 |
| #31799760 | 2 |
| #568×C277 | 2 |
| #1903 | 277 |