Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
216 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. C2×D4016 | C2 | semidirect |
| 2. C2×#22548656 | C2 | semidirect |
| 3. #30632062 | C2 | semidirect |
| 4. C16×Dic251 | C2 | semidirect |
| 5. C2×D16×C251 | C2 | semidirect |
| 23. C251⋊C16 | D4 | semidirect |
| 28. C16×C251 | D4 | semidirect |
| 48. Dic251 | D16 | semidirect |
| 53. C251 | #2246 | semidirect |
| 57. C2×D16 | D251 | semidirect |
| 82. C16 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4016 | 2 |
| C2×#22548656 | 2 |
| #30632062 | 2 |
| C16×Dic251 | 2 |
| C2×D16×C251 | 2 |
| #2246 | 251 |