Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
| 4. M16×Dic277 | C2 | semidirect |
| 5. #31799772 | C2 | semidirect |
| 6. #31799761 | C2 | semidirect |
| 15. #22579799 | C4 | semidirect |
| 16. #22579797 | C4 | semidirect |
| 95. C277 | #1932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31800050 | 2 |
| C2×#22579807 | 2 |
| #31799986 | 2 |
| M16×Dic277 | 2 |
| #31799772 | 2 |
| #31799761 | 2 |
| #421×C277 | 2 |
| #1932 | 277 |