Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
176 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 55 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. #30632035 | C2 | semidirect |
| 3. D4×C251⋊C8 | C2 | semidirect |
| 4. #30631437 | C2 | semidirect |
| 5. #30631436 | C2 | semidirect |
| 6. #30631430 | C2 | semidirect |
| 7. #476×C251 | C2 | semidirect |
| 82. C251 | #1677 | semidirect |
| 85. #476 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632035 | 2 |
| #30631882 | 2 |
| D4×C251⋊C8 | 2 |
| #30631437 | 2 |
| #30631436 | 2 |
| #30631430 | 2 |
| #476×C251 | 2 |
| #1677 | 251 |