Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
278 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
| 5. #31799767 | C2 | semidirect |
| 6. #31799766 | C2 | semidirect |
| 7. C2×#108×C277 | C2 | semidirect |
| 99. C2×D277 | #108 | semidirect |
| 113. C277 | #1855 | semidirect |
| 117. C2×#108 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D277 | 2 |
| C2×#22579815 | 2 |
| #31799965 | 2 |
| C2×#22579792 | 2 |
| #31799767 | 2 |
| #31799766 | 2 |
| C2×#108×C277 | 2 |
| #1855 | 277 |