Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
142 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 142 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 |
|---|---|---|
| 2. #31799805 | C2 | semidirect |
| 4. #31799778 | C2 | semidirect |
| 5. #500×C277 | C2 | semidirect |
| 56. C277 | #2243 | semidirect |
| 58. #500 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31800386 | 2 |
| #31799805 | 2 |
| #31799802 | 2 |
| #31799778 | 2 |
| #500×C277 | 2 |
| #2243 | 277 |