Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
488 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 2. #30631741 | C2 | direct (N × H) |
| 3. C2×Dic251⋊C8 | C2 | semidirect |
| 5. C2×#22548625 | C2 | semidirect |
| 16. Dic251⋊C8 | C22 | semidirect |
| 18. #22548625 | C22 | semidirect |
| 86. C2×C251 | #432 | semidirect |
| 90. C251 | C2×#432 | semidirect |
| 177. C2 | #30631741 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic251 | 2 |
| #30631741 | 2 |
| C2×Dic251⋊C8 | 2 |
| C2×C22⋊(C251⋊C8) | 2 |
| C2×#22548625 | 2 |
| C2×C22⋊C8×C251 | 2 |
| C2×#432 | 251 |