Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 396 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. #30632407 | C2 | semidirect |
| 2. #30632033 | C2 | semidirect |
| 3. #30632008 | C2 | semidirect |
| 4. #30631972 | C2 | semidirect |
| 5. #30631914 | C2 | semidirect |
| 6. #30631884 | C2 | semidirect |
| 7. #30631849 | C2 | semidirect |
| 8. C4×#16860800 | C2 | semidirect |
| 9. D4×C251⋊C8 | C2 | semidirect |
| 10. #30631683 | C2 | semidirect |
| 127. C251 | #3304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632407 | 2 |
| #30632033 | 2 |
| #30632008 | 2 |
| #30631972 | 2 |
| #30631914 | 2 |
| #30631884 | 2 |
| #30631849 | 2 |
| C4×#16860800 | 2 |
| D4×C251⋊C8 | 2 |
| #30631683 | 2 |
| #550×C251 | 2 |
| #3304 | 251 |