Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
432 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 205 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. #30631456 | C2 | direct (N × H) |
| 6. C2×#16860794 | C4 | semidirect |
| 17. #16860794 | C2×C4 | semidirect |
| 77. C2×C251 | #343 | semidirect |
| 81. C251 | C2×#343 | semidirect |
| 159. C2 | #30631456 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860794 | 2 |
| #30631456 | 2 |
| C22×C4⋊C4×C251 | 2 |
| C2×#343 | 251 |