Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 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. #30632244 | C2 | semidirect |
| 2. #30632046 | C2 | semidirect |
| 3. #30632041 | C2 | semidirect |
| 4. #30631696 | C2 | semidirect |
| 6. C4×#16860794 | C2 | semidirect |
| 9. #22548715 | C22 | semidirect |
| 10. #22548707 | C22 | semidirect |
| 14. #22548639 | C22 | semidirect |
| 16. #22548626 | C22 | semidirect |
| 17. C4×C251⋊C8 | C22 | semidirect |
| 83. C251 | #3140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632244 | 2 |
| #30632046 | 2 |
| #30632041 | 2 |
| #30631696 | 2 |
| #30631692 | 2 |
| C4×#16860794 | 2 |
| C2×#124×C251 | 2 |
| #3140 | 251 |