Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
504 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 96 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. #21461123 | C2 | semidirect |
| 4. #21461063 | C2 | semidirect |
| 5. #21460659 | C2 | semidirect |
| 6. #21460645 | C2 | semidirect |
| 89. C2×Dic122 | M16 | semidirect |
| 115. C2×#92418 | M16 | semidirect |
| 211. C61 | #9091 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462681 | 2 |
| #21461123 | 2 |
| #21461118 | 2 |
| #21461063 | 2 |
| #21460659 | 2 |
| #21460645 | 2 |
| C2×#16839859 | 2 |
| #9091 | 61 |