Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
216 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 77 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. #31800051 | C2 | semidirect |
| 4. M16×Dic277 | C2 | semidirect |
| 5. #31799774 | C2 | semidirect |
| 6. #31799763 | C2 | semidirect |
| 21. #101×C277 | C4 | semidirect |
| 22. #100×C277 | C4 | semidirect |
| 95. C277 | #1932 | semidirect |
| 115. #101 | Dic277 | semidirect |
| 116. #100 | Dic277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31800051 | 2 |
| #31800019 | 2 |
| C2×#22579807 | 2 |
| M16×Dic277 | 2 |
| #31799774 | 2 |
| #31799763 | 2 |
| #413×C277 | 2 |
| #1932 | 277 |