Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
296 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 83 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×#22579815 | C2 | semidirect |
| 4. C2×#22579799 | C2 | semidirect |
| 6. #31799958 | C2 | semidirect |
| 7. #419×C277 | C2 | semidirect |
| 12. C2×#17984550 | C4 | semidirect |
| 106. C277 | #1977 | semidirect |
| 110. #419 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#17984550 | 2 |
| C2×#22579815 | 2 |
| #31800006 | 2 |
| C2×#22579799 | 2 |
| C2×#22579796 | 2 |
| #31799958 | 2 |
| #419×C277 | 2 |
| #1977 | 277 |