Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
280 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 280 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 |
|---|---|---|
| 3. Q8⋊(C251⋊C8) | C2 | direct (N × H) |
| 26. C2×Q8×C251 | C8 | semidirect |
| 48. Q8×C251 | C2×C8 | semidirect |
| 78. C2×C251 | Q8⋊C8 | semidirect |
| 82. C251 | C2×Q8⋊C8 | semidirect |
| 105. C2×Q8 | C251⋊C8 | semidirect |
| 129. Q8 | C2×C251⋊C8 | semidirect |
| 161. C2 | Q8⋊(C251⋊C8) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C251⋊C8) | 2 |
| C2×C4×C251⋊C8 | 2 |
| Q8⋊(C251⋊C8) | 2 |
| C2×C4×Q8×C251 | 2 |
| C2×Q8⋊C8 | 251 |