Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
412 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 99 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×#22551514 | C2 | semidirect |
| 3. C2×#22551513 | C2 | semidirect |
| 4. C2×#22551512 | C2 | semidirect |
| 5. C2×#22551502 | C2 | semidirect |
| 6. #30656602 | C2 | semidirect |
| 7. C2×#102×C257 | C2 | semidirect |
| 12. #22551588 | C4 | semidirect |
| 38. C2×#14523339 | D4 | semidirect |
| 54. C2×C8×C257 | D4 | semidirect |
| 121. C257 | #1961 | semidirect |
| 127. C2×#102 | D257 | semidirect |
| 172. 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×#22551588 | 2 |
| C2×#22551514 | 2 |
| C2×#22551513 | 2 |
| C2×#22551512 | 2 |
| C2×#22551502 | 2 |
| #30656602 | 2 |
| C2×#102×C257 | 2 |
| #1961 | 257 |