Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
356 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 153 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. #30632091 | C2 | semidirect |
| 3. #30632088 | C2 | semidirect |
| 4. #30632087 | C2 | semidirect |
| 5. #30632084 | C2 | semidirect |
| 31. C2×C251⋊C8 | Q8 | semidirect |
| 44. C2×C8×C251 | Q8 | semidirect |
| 78. C251 | #3160 | semidirect |
| 114. C2×C8 | Dic502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632240 | 2 |
| #30632091 | 2 |
| #30632088 | 2 |
| #30632087 | 2 |
| #30632084 | 2 |
| #30631725 | 2 |
| #30631723 | 2 |
| C2×C8×Dic251 | 2 |
| #427×C251 | 2 |
| #3160 | 251 |