Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
140 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 3. #30656566 | C2 | semidirect |
| 54. C257 | #2161 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551532 | 2 |
| C2×#22551528 | 2 |
| #30656566 | 2 |
| C2×#108×C257 | 2 |
| #2161 | 257 |