Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
272 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 13. Dic251⋊C8 | C4 | semidirect |
| 15. C8×Dic251 | C4 | semidirect |
| 65. C8×C251 | C4⋊C4 | semidirect |
| 78. Dic251 | #97 | semidirect |
| 84. C251 | #1770 | semidirect |
| 150. C8 | Dic251⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic251⋊C8 | 2 |
| C2×#22548625 | 2 |
| C2×C8×Dic251 | 2 |
| C4×Dic251⋊C4 | 2 |
| #30631442 | 2 |
| #30631441 | 2 |
| C2×#97×C251 | 2 |
| #1770 | 251 |