Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 123 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. #30632407 | C2 | semidirect |
| 3. #30632034 | C2 | semidirect |
| 4. #30632012 | C2 | semidirect |
| 5. #30631973 | C2 | semidirect |
| 6. #30631916 | C2 | semidirect |
| 7. #30631888 | C2 | semidirect |
| 8. #30631851 | C2 | semidirect |
| 9. C4×Dic1004 | C2 | semidirect |
| 10. #30631684 | C2 | semidirect |
| 11. C8×D4×C251 | C2 | semidirect |
| 127. C251 | #3304 | semidirect |
| 138. C8×D4 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632407 | 2 |
| #30632358 | 2 |
| #30632034 | 2 |
| #30632012 | 2 |
| #30631973 | 2 |
| #30631916 | 2 |
| #30631888 | 2 |
| #30631851 | 2 |
| C4×Dic1004 | 2 |
| #30631684 | 2 |
| C8×D4×C251 | 2 |
| #3304 | 251 |