Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
384 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 3. C2×C4×C251⋊C8 | C2 | semidirect |
| 4. #30631442 | C2 | semidirect |
| 7. C22×C251⋊C8 | C4 | semidirect |
| 11. C22⋊(C251⋊C8) | C4 | semidirect |
| 33. C22⋊C4×C251 | C8 | semidirect |
| 38. C251⋊C8 | C22⋊C4 | direct (N × H) |
| 51. C2×C4×C251 | C2×C8 | semidirect |
| 59. C22×C251 | C4×C8 | semidirect |
| 74. C251 | C8×C22⋊C4 | semidirect |
| 108. C22⋊C4 | C251⋊C8 | direct (N × H) |
| 123. C2×C4 | C2×C251⋊C8 | semidirect |
| 134. C22 | C4×C251⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C251⋊C8 | 2 |
| C2×C22⋊(C251⋊C8) | 2 |
| C2×C4×C251⋊C8 | 2 |
| #30631442 | 2 |
| C4×C22⋊C4×C251 | 2 |
| C8×C22⋊C4 | 251 |