Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
292 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 6. C4⋊(C251⋊C8) | C4 | semidirect |
| 51. C4×C251 | #97 | semidirect |
| 59. C251 | #1767 | semidirect |
| 111. C4 | #22548626 | semidirect |
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×#22548626 | 2 |
| #30631442 | 2 |
| C43×C251 | 2 |
| #1767 | 251 |