Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
460 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×Dic1004 | C2 | semidirect |
| 3. #30631945 | C2 | semidirect |
| 4. #30631928 | C2 | semidirect |
| 5. #30631725 | C2 | semidirect |
| 6. #30631697 | C2 | semidirect |
| 88. C251 | #3059 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic1004 | 2 |
| #30632258 | 2 |
| #30631945 | 2 |
| #30631928 | 2 |
| #30631725 | 2 |
| #30631697 | 2 |
| C2×#131×C251 | 2 |
| #3059 | 251 |