Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
896 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 896 conjugacy classes of subgroups — too many to draw. Only its 469 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. C251⋊#564 | C2 | direct (N × H) |
| 58. C2×C251 | #564 | semidirect |
| 61. C251 | C2×#564 | semidirect |
| 120. C2 | C251⋊#564 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C251⋊#564 | 2 |
| C2×#22548707 | 2 |
| C2×#22548706 | 2 |
| C2×#22548705 | 2 |
| C2×#125×C251 | 2 |
| C2×#564 | 251 |