Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
424 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 197 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. #30632083 | C2 | direct (N × H) |
| 23. C2×C251⋊C8 | Q8 | semidirect |
| 42. C251⋊C8 | C2×Q8 | semidirect |
| 64. C2×C251 | #498 | semidirect |
| 68. C251 | C2×#498 | semidirect |
| 133. C2 | #30632083 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548715 | 2 |
| #30632083 | 2 |
| C2×#22548646 | 2 |
| C2×C4×C251⋊C8 | 2 |
| C2×C4⋊Q8×C251 | 2 |
| C2×#498 | 251 |