Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
196 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 77 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. C8×D1004 | C2 | semidirect |
| 3. #30631439 | C2 | semidirect |
| 4. D4⋊(C251⋊C8) | C2 | semidirect |
| 5. #30631414 | C2 | semidirect |
| 6. C8×C251⋊C8 | C2 | semidirect |
| 7. C8×D4×C251 | C2 | semidirect |
| 25. #16860795 | C8 | direct (N × H) |
| 44. D1004 | C2×C8 | semidirect |
| 51. C251⋊C8 | C2×C8 | semidirect |
| 54. D4×C251 | C2×C8 | semidirect |
| 63. C8×C251 | D8 | semidirect |
| 83. C251 | C8×D8 | semidirect |
| 87. C8×D4 | D251 | semidirect |
| 131. D4 | C8×D251 | semidirect |
| 147. C8 | #16860795 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16860795 | 2 |
| C8×D1004 | 2 |
| #30631439 | 2 |
| D4⋊(C251⋊C8) | 2 |
| #30631414 | 2 |
| C8×C251⋊C8 | 2 |
| C8×D4×C251 | 2 |
| C8×D8 | 251 |