Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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. C2×C4×Dic502 | C2 | semidirect |
| 2. #30632020 | C2 | semidirect |
| 4. #30631991 | C2 | semidirect |
| 5. #30631906 | C2 | semidirect |
| 6. #30631842 | C2 | semidirect |
| 8. #30631792 | C2 | semidirect |
| 9. #30631787 | C2 | semidirect |
| 10. #30631744 | C2 | semidirect |
| 131. C251 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic502 | 2 |
| #30632020 | 2 |
| #30632003 | 2 |
| #30631991 | 2 |
| #30631906 | 2 |
| #30631842 | 2 |
| #30631825 | 2 |
| #30631792 | 2 |
| #30631787 | 2 |
| #30631744 | 2 |
| #529×C251 | 2 |
| #3117 | 251 |