Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
344 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 4. #30656500 | C2 | semidirect |
| 5. #30656499 | C2 | semidirect |
| 6. #30656499 | C2 | semidirect |
| 7. #340×C257 | C2 | semidirect |
| 15. C4⋊C4×D257 | C4 | semidirect |
| 121. C257 | #1823 | semidirect |
| 129. #340 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×D257 | 2 |
| C2×#22551504 | 2 |
| #30656594 | 2 |
| #30656500 | 2 |
| #30656499 | 2 |
| #340×C257 | 2 |
| #1823 | 257 |