Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
284 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. C2×#22579790 | C2 | semidirect |
| 5. #31799901 | C2 | semidirect |
| 6. #31799764 | C2 | semidirect |
| 7. #340×C277 | C2 | semidirect |
| 16. #22579800 | C4 | semidirect |
| 118. C277 | #1936 | semidirect |
| 126. #340 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22579802 | 2 |
| C2×#22579800 | 2 |
| C2×#22579790 | 2 |
| #31799903 | 2 |
| #31799901 | 2 |
| #31799764 | 2 |
| #340×C277 | 2 |
| #1936 | 277 |