Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 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. #30632037 | C2 | semidirect |
| 3. #30631979 | C2 | semidirect |
| 4. #30631432 | C2 | semidirect |
| 5. #30631417 | C2 | semidirect |
| 90. C251 | #1637 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic502 | 2 |
| #30632037 | 2 |
| #30631979 | 2 |
| #30631432 | 2 |
| #30631417 | 2 |
| D4⋊(C251⋊C8) | 2 |
| #476×C251 | 2 |
| #1637 | 251 |