Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
146 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 35 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 |
|---|---|---|
| 4. C2×C4⋊Dic251 | C4 | semidirect |
| 8. C251⋊#95 | C4 | semidirect |
| 69. C251 | #1344 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631612 | 2 |
| #30631454 | 2 |
| #323×C251 | 2 |
| #1344 | 251 |