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. #30632357 | C2 | semidirect |
| 2. D4×Dic502 | C2 | semidirect |
| 3. #30632033 | C2 | semidirect |
| 4. #30632032 | C2 | semidirect |
| 5. #30631968 | C2 | semidirect |
| 6. #30631965 | C2 | semidirect |
| 7. #30631880 | C2 | semidirect |
| 8. #30631811 | C2 | semidirect |
| 9. D8×Dic251 | C2 | semidirect |
| 10. C4×#16860795 | C2 | semidirect |
| 11. #459×C251 | C2 | semidirect |
| 78. Dic502 | D8 | semidirect |
| 99. D4×C251 | #41 | semidirect |
| 131. C251 | #3358 | semidirect |
| 140. #459 | D251 | semidirect |
| 222. D4 | #16860809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632357 | 2 |
| D4×Dic502 | 2 |
| #30632033 | 2 |
| #30632032 | 2 |
| #30631968 | 2 |
| #30631965 | 2 |
| #30631880 | 2 |
| #30631811 | 2 |
| D8×Dic251 | 2 |
| C4×#16860795 | 2 |
| #459×C251 | 2 |
| #3358 | 251 |