Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
158 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 3. Q16×Dic257 | C2 | semidirect |
| 4. #30656555 | C2 | semidirect |
| 5. #30656541 | C2 | semidirect |
| 7. C2×Q32×C257 | C2 | semidirect |
| 72. C257 | #2211 | semidirect |
| 74. C2×Q32 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551535 | 2 |
| #30657122 | 2 |
| Q16×Dic257 | 2 |
| #30656555 | 2 |
| #30656541 | 2 |
| #30656539 | 2 |
| C2×Q32×C257 | 2 |
| #2211 | 257 |