Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
182 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 2. #30631764 | C2 | semidirect |
| 3. D4×C251⋊C8 | C2 | semidirect |
| 4. #30631439 | C2 | semidirect |
| 5. #30631416 | C2 | semidirect |
| 6. #30631409 | C2 | semidirect |
| 7. D4⋊C8×C251 | C2 | semidirect |
| 52. C251⋊C8 | D8 | semidirect |
| 55. D4×C251 | M16 | semidirect |
| 83. C251 | #1581 | semidirect |
| 90. D4⋊C8 | D251 | semidirect |
| 131. D4 | #16860793 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16860795 | 2 |
| #30631764 | 2 |
| D4×C251⋊C8 | 2 |
| #30631439 | 2 |
| #30631416 | 2 |
| #30631409 | 2 |
| D4⋊C8×C251 | 2 |
| #1581 | 251 |