Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 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. #30657088 | C2 | semidirect |
| 3. #30657032 | C2 | semidirect |
| 5. #30656482 | C2 | semidirect |
| 7. Q8⋊C8×C257 | C2 | semidirect |
| 90. C257 | #1637 | semidirect |
| 97. Q8⋊C8 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D1028 | 2 |
| #30657088 | 2 |
| #30657032 | 2 |
| #30657028 | 2 |
| #30656482 | 2 |
| #30656466 | 2 |
| Q8⋊C8×C257 | 2 |
| #1637 | 257 |