Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
384 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 173 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. #30631747 | C2 | semidirect |
| 3. #30631743 | C2 | semidirect |
| 4. #30631714 | C2 | semidirect |
| 7. M16×Dic251 | C2 | semidirect |
| 8. C2×#22548625 | C2 | semidirect |
| 9. #424×C251 | C2 | semidirect |
| 93. C251 | #2923 | semidirect |
| 99. #424 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632155 | 2 |
| #30631747 | 2 |
| #30631743 | 2 |
| #30631714 | 2 |
| #30631655 | 2 |
| #30631653 | 2 |
| M16×Dic251 | 2 |
| C2×#22548625 | 2 |
| #424×C251 | 2 |
| #2923 | 251 |