Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
504 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 193 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. #30656633 | C2 | semidirect |
| 4. #30656604 | C2 | semidirect |
| 5. C4⋊C4×Dic257 | C2 | semidirect |
| 6. #30656588 | C2 | semidirect |
| 9. #22551551 | C4 | semidirect |
| 94. C257 | #2347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551551 | 2 |
| #30656633 | 2 |
| #30656625 | 2 |
| #30656604 | 2 |
| C4⋊C4×Dic257 | 2 |
| #30656588 | 2 |
| C4×C22⋊Dic257 | 2 |
| #380×C257 | 2 |
| #2347 | 257 |