Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
210 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 1. #31800050 | C2 | semidirect |
| 2. #31800028 | C2 | semidirect |
| 6. #31799758 | C2 | semidirect |
| 7. #424×C277 | C2 | semidirect |
| 89. C277 | #2098 | semidirect |
| 93. #424 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31800050 | 2 |
| #31800028 | 2 |
| #31800020 | 2 |
| #31800018 | 2 |
| #31799968 | 2 |
| #31799758 | 2 |
| #424×C277 | 2 |
| #2098 | 277 |