Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
236 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 1. C2×#22551532 | C2 | semidirect |
| 2. #30656519 | C2 | direct (N × H) |
| 5. #22551532 | C22 | semidirect |
| 70. C2×C257 | #349 | semidirect |
| 72. C257 | C2×#349 | semidirect |
| 143. C2 | #30656519 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551532 | 2 |
| #30656519 | 2 |
| C22×M16×C257 | 2 |
| C2×#349 | 257 |