Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
270 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. C2×#22579815 | C2 | semidirect |
| 3. #31800029 | C2 | semidirect |
| 6. #31799757 | C2 | semidirect |
| 7. #339×C277 | C2 | semidirect |
| 20. #22579803 | C4 | semidirect |
| 21. #22579803 | C4 | semidirect |
| 22. #22579800 | C4 | semidirect |
| 23. #22579800 | C4 | semidirect |
| 109. C277 | #1866 | semidirect |
| 116. #339 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22579888 | 2 |
| C2×#22579815 | 2 |
| #31800029 | 2 |
| C2×#22579808 | 2 |
| #31799996 | 2 |
| #31799757 | 2 |
| #339×C277 | 2 |
| #1866 | 277 |