Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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×#22579825 | C2 | semidirect |
| 3. #31800243 | C2 | semidirect |
| 4. #31799804 | C2 | semidirect |
| 5. C22⋊C16×C277 | C2 | semidirect |
| 7. C2×Dic1108 | C22 | semidirect |
| 13. #22579814 | C22 | semidirect |
| 16. C2×C16×C277 | C22 | semidirect |
| 55. C22×C277 | SD32 | semidirect |
| 71. C277 | #2187 | semidirect |
| 77. C22⋊C16 | D277 | semidirect |
| 86. C2×C16 | C2×D277 | semidirect |
| 131. C22 | #22579825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D2216 | 2 |
| C2×#22579825 | 2 |
| #31800243 | 2 |
| #31799804 | 2 |
| C22⋊C16×C277 | 2 |
| #2187 | 277 |