Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
376 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 113 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×#22548647 | C2 | semidirect |
| 2. C2×#22548636 | C2 | semidirect |
| 3. C2×#22548625 | C2 | semidirect |
| 4. #30631590 | C2 | semidirect |
| 16. C2×D8×C251 | C4 | semidirect |
| 61. C8×C251 | C22⋊C4 | semidirect |
| 82. C251 | #1972 | semidirect |
| 92. C2×D8 | Dic251 | semidirect |
| 144. C8 | C22⋊Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548647 | 2 |
| C2×#22548636 | 2 |
| C2×#22548625 | 2 |
| #30631590 | 2 |
| C22×D8×C251 | 2 |
| #1972 | 251 |