Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
162 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 67 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. Q16×Dic251 | C2 | semidirect |
| 3. #30631515 | C2 | semidirect |
| 4. #30631491 | C2 | semidirect |
| 6. C16×Dic251 | C2 | semidirect |
| 18. SD32×C251 | C4 | semidirect |
| 32. Q16×C251 | C2×C4 | semidirect |
| 36. C16×C251 | C2×C4 | semidirect |
| 62. Dic251 | SD32 | direct (N × H) |
| 67. C251 | C4×SD32 | semidirect |
| 80. SD32 | Dic251 | direct (N × H) |
| 92. Q16 | C2×Dic251 | semidirect |
| 104. C16 | C2×Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×Dic251 | 2 |
| D8×Dic251 | 2 |
| #30631515 | 2 |
| #30631491 | 2 |
| #30631488 | 2 |
| C16×Dic251 | 2 |
| C2×SD32×C251 | 2 |
| C4×SD32 | 251 |