Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 1. D4×Dic502 | C2 | semidirect |
| 2. #30632039 | C2 | semidirect |
| 3. #30632017 | C2 | semidirect |
| 4. #30631969 | C2 | semidirect |
| 5. #30631914 | C2 | semidirect |
| 6. #30631892 | C2 | semidirect |
| 7. #30631825 | C2 | semidirect |
| 8. C4×#16860798 | C2 | semidirect |
| 9. D4×C251⋊C8 | C2 | semidirect |
| 10. C2×#22548638 | C2 | semidirect |
| 81. Dic502 | #41 | semidirect |
| 95. D4×C251 | SD16 | semidirect |
| 128. C251 | #3298 | semidirect |
| 217. D4 | #16860798 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic502 | 2 |
| #30632039 | 2 |
| #30632017 | 2 |
| #30631969 | 2 |
| #30631914 | 2 |
| #30631892 | 2 |
| #30631825 | 2 |
| C4×#16860798 | 2 |
| D4×C251⋊C8 | 2 |
| C2×#22548638 | 2 |
| #547×C251 | 2 |
| #3298 | 251 |