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 |
|---|---|---|
| 2. C2×C4×Dic502 | C2 | semidirect |
| 3. #30632023 | C2 | semidirect |
| 5. #30631995 | C2 | semidirect |
| 6. #30631910 | C2 | semidirect |
| 7. #30631845 | C2 | semidirect |
| 9. #30631795 | C2 | semidirect |
| 10. #30631789 | C2 | semidirect |
| 11. #432×C251 | C2 | semidirect |
| 131. C251 | #3117 | semidirect |
| 143. #432 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632221 | 2 |
| C2×C4×Dic502 | 2 |
| #30632023 | 2 |
| #30632006 | 2 |
| #30631995 | 2 |
| #30631910 | 2 |
| #30631845 | 2 |
| #30631828 | 2 |
| #30631795 | 2 |
| #30631789 | 2 |
| #432×C251 | 2 |
| #3117 | 251 |