Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
184 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 184 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 |
|---|---|---|
| 2. C4⋊(C251⋊C16) | C2 | direct (N × H) |
| 25. C2×C4×C251 | C16 | semidirect |
| 42. C4×C251 | C2×C16 | semidirect |
| 45. C2×C251 | C4⋊C16 | semidirect |
| 49. C251 | C2×C4⋊C16 | semidirect |
| 75. C2×C4 | C251⋊C16 | semidirect |
| 92. C4 | C2×C251⋊C16 | semidirect |
| 95. C2 | C4⋊(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 |
| C4⋊(C251⋊C16) | 2 |
| C2×C4×C8×C251 | 2 |
| C2×C4⋊C16 | 251 |