Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
232 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 86 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. #21462233 | C2 | semidirect |
| 3. #21460849 | C2 | semidirect |
| 4. #21460786 | C2 | semidirect |
| 6. #21460734 | C2 | semidirect |
| 52. #11758200 | C16 | semidirect |
| 80. Dic122 | C2×C16 | semidirect |
| 86. #92418 | C2×C16 | semidirect |
| 128. C61 | SD16⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462233 | 2 |
| D4×#11758187 | 2 |
| #21460849 | 2 |
| #21460786 | 2 |
| D4⋊#11758187 | 2 |
| #21460734 | 2 |
| #21444622 | 2 |
| SD16⋊C16 | 61 |