Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
180 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 101 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. #30631439 | C2 | semidirect |
| 4. #30631437 | C2 | semidirect |
| 21. C2×C251⋊C8 | C8 | semidirect |
| 66. C251 | #1564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631740 | 2 |
| C2×C4×C251⋊C8 | 2 |
| #30631439 | 2 |
| #30631437 | 2 |
| #431×C251 | 2 |
| #1564 | 251 |