Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 1. #30657457 | C2 | semidirect |
| 2. #30657084 | C2 | semidirect |
| 3. #30656938 | C2 | semidirect |
| 5. #30656482 | C2 | semidirect |
| 6. #30656469 | C2 | semidirect |
| 7. D4⋊C8×C257 | C2 | semidirect |
| 95. C257 | #1628 | semidirect |
| 103. D4⋊C8 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30657457 | 2 |
| #30657084 | 2 |
| #30656938 | 2 |
| #30656932 | 2 |
| #30656482 | 2 |
| #30656469 | 2 |
| D4⋊C8×C257 | 2 |
| #1628 | 257 |