Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
368 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 85 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×#22551523 | C2 | semidirect |
| 3. C2×#22551514 | C2 | semidirect |
| 4. C2×#22551512 | C2 | semidirect |
| 5. C2×#22551504 | C2 | semidirect |
| 6. #30656594 | C2 | semidirect |
| 7. #340×C257 | C2 | semidirect |
| 46. C2×#14523339 | D4 | semidirect |
| 143. C257 | #2034 | semidirect |
| 151. #340 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551567 | 2 |
| C2×#22551523 | 2 |
| C2×#22551514 | 2 |
| C2×#22551512 | 2 |
| C2×#22551504 | 2 |
| #30656594 | 2 |
| #340×C257 | 2 |
| #2034 | 257 |