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 |
| 3. #30632038 | C2 | semidirect |
| 4. #30632018 | C2 | semidirect |
| 5. #30631973 | C2 | semidirect |
| 6. #30631916 | C2 | semidirect |
| 7. #30631893 | C2 | semidirect |
| 8. #30631828 | C2 | semidirect |
| 9. C4×#16860799 | C2 | semidirect |
| 10. C2×#22548640 | C2 | semidirect |
| 11. C8×D4×C251 | C2 | semidirect |
| 83. Dic502 | #41 | semidirect |
| 96. D4×C251 | SD16 | semidirect |
| 128. C251 | #3298 | semidirect |
| 139. C8×D4 | D251 | semidirect |
| 217. D4 | #16860799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic502 | 2 |
| #30632341 | 2 |
| #30632038 | 2 |
| #30632018 | 2 |
| #30631973 | 2 |
| #30631916 | 2 |
| #30631893 | 2 |
| #30631828 | 2 |
| C4×#16860799 | 2 |
| C2×#22548640 | 2 |
| C8×D4×C251 | 2 |
| #3298 | 251 |