Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
412 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 412 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×#22551551 | C2 | semidirect |
| 3. C2×#22551514 | C2 | semidirect |
| 4. #30656500 | C2 | semidirect |
| 5. C2×C22⋊C8×C257 | C2 | semidirect |
| 9. #22551566 | C4 | semidirect |
| 32. C4⋊Dic257 | D4 | semidirect |
| 102. C257 | #1875 | semidirect |
| 107. C2×C22⋊C8 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551566 | 2 |
| C2×#22551551 | 2 |
| C2×#22551514 | 2 |
| #30656500 | 2 |
| C2×C22⋊C8×C257 | 2 |
| #1875 | 257 |