Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
196 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 89 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. D4×C251⋊C8 | C2 | semidirect |
| 2. #30631440 | C2 | semidirect |
| 3. D4⋊(C251⋊C8) | C2 | semidirect |
| 4. C8×C251⋊C8 | C2 | semidirect |
| 23. D8×C251 | C8 | semidirect |
| 32. C251⋊C8 | D8 | direct (N × H) |
| 35. D4×C251 | C2×C8 | semidirect |
| 43. C8×C251 | C2×C8 | semidirect |
| 58. C251 | C8×D8 | semidirect |
| 77. D8 | C251⋊C8 | direct (N × H) |
| 90. D4 | C2×C251⋊C8 | semidirect |
| 102. C8 | C2×C251⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×C251⋊C8 | 2 |
| #30631440 | 2 |
| D4⋊(C251⋊C8) | 2 |
| C8×C251⋊C8 | 2 |
| C4×D8×C251 | 2 |
| C8×D8 | 251 |