Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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. C4×Dic1108 | C2 | semidirect |
| 4. #31799830 | C2 | semidirect |
| 5. #31799807 | C2 | semidirect |
| 7. C4×C16×C277 | C2 | semidirect |
| 12. #22579825 | C4 | direct (N × H) |
| 24. Dic1108 | C2×C4 | semidirect |
| 36. C16×C277 | C2×C4 | semidirect |
| 57. C4×C277 | SD32 | semidirect |
| 67. C277 | C4×SD32 | semidirect |
| 75. C4×C16 | D277 | semidirect |
| 104. C16 | C4×D277 | semidirect |
| 128. C4 | #22579825 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22579825 | 2 |
| C4×Dic1108 | 2 |
| C4×D2216 | 2 |
| #31799830 | 2 |
| #31799807 | 2 |
| #31799804 | 2 |
| C4×C16×C277 | 2 |
| C4×SD32 | 277 |