Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
316 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 125 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×#22548649 | C2 | semidirect |
| 2. C2×#22548647 | C2 | semidirect |
| 4. #30631450 | C2 | semidirect |
| 15. C2×M16×C251 | C4 | semidirect |
| 67. C8×C251 | C22⋊C4 | semidirect |
| 91. C251 | #1809 | semidirect |
| 101. C2×M16 | Dic251 | semidirect |
| 159. C8 | C22⋊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 |
| #30631547 | 2 |
| #30631450 | 2 |
| C22×M16×C251 | 2 |
| #1809 | 251 |