Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
244 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 67 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. #31799772 | C2 | semidirect |
| 5. #31799762 | C2 | semidirect |
| 6. #31799758 | C2 | semidirect |
| 7. #533×C277 | C2 | semidirect |
| 27. C2×Dic554 | Q8 | semidirect |
| 28. C2×D1108 | Q8 | semidirect |
| 101. C277 | #2031 | semidirect |
| 103. #533 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31800020 | 2 |
| C2×#22579808 | 2 |
| #31799975 | 2 |
| #31799772 | 2 |
| #31799762 | 2 |
| #31799758 | 2 |
| #533×C277 | 2 |
| #2031 | 277 |