Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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. #30632315 | C2 | semidirect |
| 3. #30631997 | C2 | semidirect |
| 4. #30631986 | C2 | semidirect |
| 5. #30631981 | C2 | semidirect |
| 6. #30631966 | C2 | semidirect |
| 7. C2×#22548648 | C2 | semidirect |
| 8. #30631715 | C2 | semidirect |
| 11. #428×C251 | C2 | semidirect |
| 42. #16860810 | Q8 | semidirect |
| 123. C251 | #3083 | semidirect |
| 131. #428 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632315 | 2 |
| #30632168 | 2 |
| #30631997 | 2 |
| #30631986 | 2 |
| #30631981 | 2 |
| #30631966 | 2 |
| C2×#22548648 | 2 |
| #30631715 | 2 |
| #30631689 | 2 |
| #30631681 | 2 |
| #428×C251 | 2 |
| #3083 | 251 |