Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
368 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 368 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 |
|---|---|---|
| 2. #30632092 | C2 | semidirect |
| 3. #30632067 | C2 | semidirect |
| 4. #30632038 | C2 | semidirect |
| 6. C4×Dic1004 | C2 | semidirect |
| 52. C2×C4×C251 | Q16 | semidirect |
| 77. C251 | #3170 | semidirect |
| 130. C2×C4 | Dic1004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632244 | 2 |
| #30632092 | 2 |
| #30632067 | 2 |
| #30632038 | 2 |
| #30631928 | 2 |
| C4×Dic1004 | 2 |
| C2×C4×C8×C251 | 2 |
| #3170 | 251 |