Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 3. #30632095 | C2 | semidirect |
| 4. #30632094 | C2 | semidirect |
| 5. #30632088 | C2 | semidirect |
| 6. #30632087 | C2 | semidirect |
| 48. #16860794 | Q8 | semidirect |
| 72. M16×C251 | Q8 | semidirect |
| 124. C251 | #3166 | semidirect |
| 176. M16 | Dic502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632240 | 2 |
| C2×#22548706 | 2 |
| #30632095 | 2 |
| #30632094 | 2 |
| #30632088 | 2 |
| #30632087 | 2 |
| #30631730 | 2 |
| #30631729 | 2 |
| #30631727 | 2 |
| M16×Dic251 | 2 |
| #428×C251 | 2 |
| #3166 | 251 |