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 |
|---|---|---|
| 3. #30632031 | C2 | semidirect |
| 4. #30632030 | C2 | semidirect |
| 5. #30632024 | C2 | semidirect |
| 6. #30632019 | C2 | semidirect |
| 7. #30631730 | C2 | semidirect |
| 8. #30631695 | C2 | semidirect |
| 9. C2×#22548640 | C2 | semidirect |
| 11. #427×C251 | C2 | semidirect |
| 126. C251 | #3097 | semidirect |
| 135. #427 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632263 | 2 |
| #30632167 | 2 |
| #30632031 | 2 |
| #30632030 | 2 |
| #30632024 | 2 |
| #30632019 | 2 |
| #30631730 | 2 |
| #30631695 | 2 |
| C2×#22548640 | 2 |
| #30631653 | 2 |
| #427×C251 | 2 |
| #3097 | 251 |