Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
336 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 121 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×#22548625 | C2 | semidirect |
| 5. C2×C8×Dic251 | C2 | semidirect |
| 6. #30631442 | C2 | semidirect |
| 7. #336×C251 | C2 | semidirect |
| 16. (C2×D251)⋊C8 | C4 | semidirect |
| 17. (C2×D251)⋊C8 | C4 | semidirect |
| 104. C251 | #1750 | semidirect |
| 112. #336 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548672 | 2 |
| C2×(C2×D251)⋊C8 | 2 |
| C2×#22548625 | 2 |
| C2×C8×Dic251 | 2 |
| #30631442 | 2 |
| #336×C251 | 2 |
| #1750 | 251 |