Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
248 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 14. #22548639 | C4 | semidirect |
| 105. C251 | #1935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548639 | 2 |
| C2×#22548626 | 2 |
| #30631585 | 2 |
| #30631449 | 2 |
| #391×C251 | 2 |
| #1935 | 251 |