Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
440 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 253 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. #30631811 | C2 | direct (N × H) |
| 21. C2×Dic502 | C8 | semidirect |
| 26. C2×C251⋊C8 | Q8 | semidirect |
| 40. Dic502 | C2×C8 | semidirect |
| 46. C251⋊C8 | C2×Q8 | semidirect |
| 68. C2×C251 | C8×Q8 | semidirect |
| 72. C251 | C2×C8×Q8 | semidirect |
| 141. C2 | #30631811 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic502 | 2 |
| #30631811 | 2 |
| C2×Dic251⋊C8 | 2 |
| C2×C4×C251⋊C8 | 2 |
| C2×C8×Dic251 | 2 |
| C2×C4⋊C8×C251 | 2 |
| C2×C8×Q8 | 251 |