Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
184 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #31799777 | C2 | semidirect |
| 5. C4×#17984538 | C2 | semidirect |
| 6. C16×Dic277 | C2 | semidirect |
| 7. #346×C277 | C2 | semidirect |
| 11. #22579819 | C4 | semidirect |
| 14. C16×D277 | C4 | semidirect |
| 60. C277 | #2108 | semidirect |
| 66. #346 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22579819 | 2 |
| C2×C16×D277 | 2 |
| #31799956 | 2 |
| #31799777 | 2 |
| C4×#17984538 | 2 |
| C16×Dic277 | 2 |
| #346×C277 | 2 |
| #2108 | 277 |