Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 125 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. #30632358 | C2 | semidirect |
| 2. D4×Dic502 | C2 | semidirect |
| 3. #30632034 | C2 | semidirect |
| 4. #30632032 | C2 | semidirect |
| 5. #30631967 | C2 | semidirect |
| 6. #30631966 | C2 | semidirect |
| 7. #30631882 | C2 | semidirect |
| 8. #30631880 | C2 | semidirect |
| 9. C8×Dic502 | C2 | semidirect |
| 10. #30631767 | C2 | semidirect |
| 11. C4×D8×C251 | C2 | semidirect |
| 78. Dic502 | D8 | semidirect |
| 96. D4×C251 | #41 | semidirect |
| 131. C251 | #3358 | semidirect |
| 143. C4×D8 | D251 | semidirect |
| 222. D4 | #16860810 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632358 | 2 |
| D4×Dic502 | 2 |
| #30632034 | 2 |
| #30632032 | 2 |
| #30631967 | 2 |
| #30631966 | 2 |
| #30631882 | 2 |
| #30631880 | 2 |
| C8×Dic502 | 2 |
| #30631767 | 2 |
| C4×D8×C251 | 2 |
| #3358 | 251 |