Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
312 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 97 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. #30631711 | C2 | semidirect |
| 2. C2×#22548634 | C2 | semidirect |
| 4. C4×#16860794 | C2 | semidirect |
| 80. C251 | #1967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631711 | 2 |
| C2×#22548634 | 2 |
| C2×#22548632 | 2 |
| C4×#16860794 | 2 |
| C2×#124×C251 | 2 |
| #1967 | 251 |