Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
272 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×C251⋊C16 | C2 | semidirect |
| 2. C22⋊(C251⋊C16) | C2 | direct (N × H) |
| 5. C2×C251⋊C16 | C22 | semidirect |
| 29. C23×C251 | C16 | semidirect |
| 49. C22×C251 | C2×C16 | semidirect |
| 57. C2×C251 | C22⋊C16 | semidirect |
| 61. C251 | C2×C22⋊C16 | semidirect |
| 91. C23 | C251⋊C16 | semidirect |
| 111. C22 | C2×C251⋊C16 | semidirect |
| 119. C2 | C22⋊(C251⋊C16) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C251⋊C16 | 2 |
| C22⋊(C251⋊C16) | 2 |
| C23×C8×C251 | 2 |
| C2×C22⋊C16 | 251 |