Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
300 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 21. C4×Dic251 | C8 | semidirect |
| 55. C4×C251 | C4⋊C8 | semidirect |
| 60. Dic251 | C4⋊C8 | semidirect |
| 66. C251 | #1842 | semidirect |
| 124. C4 | Dic251⋊C8 | 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×Dic251⋊C8 | 2 |
| C42×Dic251 | 2 |
| C2×C4⋊C8×C251 | 2 |
| #1842 | 251 |