Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
384 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 384 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×#22551521 | C2 | semidirect |
| 3. C2×C22⋊#14523339 | C2 | semidirect |
| 4. C2×#22551504 | C2 | semidirect |
| 5. C2×#22551504 | C2 | semidirect |
| 6. C2×#22551502 | C2 | semidirect |
| 7. C2×C22⋊C8×C257 | C2 | semidirect |
| 45. C2×#14523339 | D4 | semidirect |
| 65. C2×C8×C257 | D4 | semidirect |
| 150. C257 | #1955 | semidirect |
| 157. C2×C22⋊C8 | D257 | semidirect |
| 211. C2×C8 | C22⋊D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D257 | 2 |
| C2×#22551521 | 2 |
| C2×C22⋊#14523339 | 2 |
| C2×#22551504 | 2 |
| C2×#22551502 | 2 |
| C2×C22⋊C8×C257 | 2 |
| #1955 | 257 |