Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
384 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 384 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. C2×#22548706 | C2 | semidirect |
| 3. #30631997 | C2 | semidirect |
| 4. #30631993 | C2 | semidirect |
| 5. #30631990 | C2 | semidirect |
| 6. #30631986 | C2 | semidirect |
| 7. #30631730 | C2 | semidirect |
| 8. #30631710 | C2 | semidirect |
| 11. #428×C251 | C2 | semidirect |
| 135. C251 | #3080 | semidirect |
| 144. #428 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548706 | 2 |
| #30632155 | 2 |
| #30631997 | 2 |
| #30631993 | 2 |
| #30631990 | 2 |
| #30631986 | 2 |
| #30631730 | 2 |
| #30631710 | 2 |
| #30631689 | 2 |
| #30631686 | 2 |
| #428×C251 | 2 |
| #3080 | 251 |