Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
256 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 15. #97×C251 | C4 | semidirect |
| 45. C8×C251 | C4⋊C4 | semidirect |
| 62. C251 | #1847 | semidirect |
| 77. #97 | Dic251 | semidirect |
| 108. C8 | C4⋊Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548649 | 2 |
| C2×#22548647 | 2 |
| #30631557 | 2 |
| #30631553 | 2 |
| C2×#97×C251 | 2 |
| #1847 | 251 |