Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
160 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 53 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. #31799755 | C2 | semidirect |
| 5. #31799751 | C2 | semidirect |
| 6. #31799748 | C2 | semidirect |
| 7. #487×C277 | C2 | semidirect |
| 75. C277 | #1683 | semidirect |
| 77. #487 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31800289 | 2 |
| #31800279 | 2 |
| C8×D1108 | 2 |
| #31799755 | 2 |
| #31799751 | 2 |
| #31799748 | 2 |
| #487×C277 | 2 |
| #1683 | 277 |