Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
408 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 97 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×#22551506 | C2 | semidirect |
| 3. #30656597 | C2 | semidirect |
| 4. C4×C22⋊C4×C257 | C2 | semidirect |
| 5. C22×D1028 | C4 | semidirect |
| 12. C2×C4⋊Dic257 | C4 | semidirect |
| 14. C2×#16861595 | C4 | semidirect |
| 47. C22⋊C4×C257 | D4 | semidirect |
| 104. C4×C257 | #99 | semidirect |
| 115. C257 | #1964 | semidirect |
| 120. C4×C22⋊C4 | D257 | semidirect |
| 163. C22⋊C4 | D1028 | semidirect |
| 222. C4 | #22551506 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551566 | 2 |
| C2×#22551506 | 2 |
| #30656597 | 2 |
| C4×C22⋊C4×C257 | 2 |
| #1964 | 257 |