Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 123 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. #30632415 | C2 | semidirect |
| 3. #30632037 | C2 | semidirect |
| 4. #30631994 | C2 | semidirect |
| 7. #30631894 | C2 | semidirect |
| 8. Q8×C251⋊C8 | C2 | semidirect |
| 9. C4×#16860800 | C2 | semidirect |
| 115. C251 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632415 | 2 |
| #30632041 | 2 |
| #30632037 | 2 |
| #30631994 | 2 |
| #30631967 | 2 |
| #30631906 | 2 |
| #30631894 | 2 |
| Q8×C251⋊C8 | 2 |
| C4×#16860800 | 2 |
| C4×#16860798 | 2 |
| #556×C251 | 2 |
| #3364 | 251 |