Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
280 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 12. C8×Dic251 | C4 | semidirect |
| 37. C251⋊C8 | C4⋊C4 | semidirect |
| 47. C8×C251 | C4⋊C4 | semidirect |
| 58. Dic251 | #106 | semidirect |
| 63. C251 | #1844 | semidirect |
| 111. C8 | Dic251⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548647 | 2 |
| C2×#22548646 | 2 |
| C2×C8×Dic251 | 2 |
| #30631556 | 2 |
| C2×#106×C251 | 2 |
| #1844 | 251 |