Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #30632223 | C2 | semidirect |
| 2. #30632088 | C2 | semidirect |
| 3. #30632072 | C2 | semidirect |
| 4. #30632043 | C2 | semidirect |
| 6. #30631918 | C2 | semidirect |
| 7. Q16×Dic251 | C2 | semidirect |
| 8. #30631772 | C2 | semidirect |
| 9. #30631769 | C2 | semidirect |
| 10. C2×C8×Dic251 | C2 | semidirect |
| 11. #467×C251 | C2 | semidirect |
| 118. C251 | #3168 | semidirect |
| 124. #467 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632223 | 2 |
| #30632088 | 2 |
| #30632072 | 2 |
| #30632043 | 2 |
| #30631923 | 2 |
| #30631918 | 2 |
| Q16×Dic251 | 2 |
| #30631772 | 2 |
| #30631769 | 2 |
| C2×C8×Dic251 | 2 |
| #467×C251 | 2 |
| #3168 | 251 |