Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
512 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 309 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. #30631725 | C2 | direct (N × H) |
| 3. C2×#22548649 | C2 | semidirect |
| 4. C2×#22548647 | C2 | semidirect |
| 11. #22548649 | C22 | semidirect |
| 12. #22548647 | C22 | semidirect |
| 14. C22×C8×C251 | C4 | semidirect |
| 32. C2×C8×C251 | C2×C4 | semidirect |
| 64. C2×C251 | #427 | semidirect |
| 67. C251 | C2×#427 | semidirect |
| 75. C22×C8 | Dic251 | semidirect |
| 96. C2×C8 | C2×Dic251 | semidirect |
| 132. C2 | #30631725 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548674 | 2 |
| #30631725 | 2 |
| C2×#22548649 | 2 |
| C2×#22548647 | 2 |
| C23×C8×C251 | 2 |
| C2×#427 | 251 |