Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
384 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 4. #30631979 | C2 | semidirect |
| 5. #30631898 | C2 | semidirect |
| 6. #30631897 | C2 | semidirect |
| 8. #30631781 | C2 | semidirect |
| 9. #30631779 | C2 | semidirect |
| 11. #477×C251 | C2 | semidirect |
| 99. C4×D251 | Q16 | semidirect |
| 132. C251 | #3104 | semidirect |
| 138. #477 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632242 | 2 |
| C4×Q8×D251 | 2 |
| #30632024 | 2 |
| #30631979 | 2 |
| #30631898 | 2 |
| #30631897 | 2 |
| #30631844 | 2 |
| #30631781 | 2 |
| #30631779 | 2 |
| #30631739 | 2 |
| #477×C251 | 2 |
| #3104 | 251 |