Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
292 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31799960 | C2 | semidirect |
| 4. C2×#22579791 | C2 | semidirect |
| 5. #31799766 | C2 | semidirect |
| 6. #31799762 | C2 | semidirect |
| 9. #22579887 | C4 | semidirect |
| 16. #22579804 | C4 | semidirect |
| 17. #22579801 | C4 | semidirect |
| 24. #104×C277 | C4 | semidirect |
| 98. C277 | #1765 | semidirect |
| 118. #104 | Dic277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22579887 | 2 |
| #31799998 | 2 |
| #31799960 | 2 |
| C2×#22579791 | 2 |
| #31799766 | 2 |
| #31799762 | 2 |
| C2×#104×C277 | 2 |
| #1765 | 277 |