Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
820 conjugacy classes of subgroups; only the 333 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 333 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. C2×Q8×Dic251 | C2 | semidirect |
| 2. #30631594 | C2 | semidirect |
| 14. C22×Q8×C251 | C4 | semidirect |
| 22. C22⋊Dic251 | Q8 | direct (N × H) |
| 39. C2×Dic251 | C2×Q8 | semidirect |
| 47. Q8×C251 | C22⋊C4 | semidirect |
| 57. C22×C251 | C4×Q8 | semidirect |
| 73. C251 | Q8×C22⋊C4 | semidirect |
| 81. C22×Q8 | Dic251 | semidirect |
| 115. Q8 | C22⋊Dic251 | direct (N × H) |
| 131. C22 | Q8×Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic251 | 2 |
| #30631594 | 2 |
| #30631547 | 2 |
| C4×C22⋊Dic251 | 2 |
| C23×Q8×C251 | 2 |
| Q8×C22⋊C4 | 251 |