Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
438 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 110 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×#16840685 | C2 | semidirect |
| 2. C2×#16840661 | C2 | semidirect |
| 3. C2×#16840660 | C2 | semidirect |
| 4. #21462051 | C2 | semidirect |
| 5. #21462049 | C2 | semidirect |
| 6. C2×C4×#11758187 | C2 | semidirect |
| 206. C61 | #13195 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840685 | 2 |
| C2×#16840661 | 2 |
| C2×#16840660 | 2 |
| #21462051 | 2 |
| #21462049 | 2 |
| C2×C4×#11758187 | 2 |
| C2×#16839876 | 2 |
| #13195 | 61 |