Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
256 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 3. #30631436 | C2 | semidirect |
| 4. #30631435 | C2 | semidirect |
| 5. #333×C251 | C2 | semidirect |
| 61. D251 | #333 | direct (N × H) |
| 62. C251 | C2×#333 | semidirect |
| 68. #333 | D251 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D251 | 2 |
| C4⋊C8×D251 | 2 |
| #30631436 | 2 |
| #30631435 | 2 |
| #333×C251 | 2 |
| C2×#333 | 251 |