Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
376 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 105 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×#22551512 | C2 | semidirect |
| 3. C2×#22551502 | C2 | semidirect |
| 4. #30656638 | C2 | semidirect |
| 5. C2×#106×C257 | C2 | semidirect |
| 9. C2×D2056 | C4 | semidirect |
| 61. C8×C257 | C22⋊C4 | semidirect |
| 82. C257 | #1972 | semidirect |
| 85. C2×#106 | D257 | semidirect |
| 144. C8 | #16861595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D2056 | 2 |
| C2×#22551512 | 2 |
| C2×#22551502 | 2 |
| #30656638 | 2 |
| C2×#106×C257 | 2 |
| #1972 | 257 |