Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
324 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 105 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×#22551521 | C2 | semidirect |
| 5. #30656492 | C2 | semidirect |
| 6. #30656491 | C2 | semidirect |
| 7. C2×C4⋊C8×C257 | C2 | semidirect |
| 72. C2×Dic257 | M16 | semidirect |
| 85. C2×C4×C257 | M16 | semidirect |
| 125. C257 | #1851 | semidirect |
| 129. C2×C4⋊C8 | D257 | semidirect |
| 209. C2×C4 | #16861601 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16861601 | 2 |
| C2×#22551521 | 2 |
| C2×#22551504 | 2 |
| C4×#16861595 | 2 |
| #30656492 | 2 |
| #30656491 | 2 |
| C2×C4⋊C8×C257 | 2 |
| #1851 | 257 |