Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
2022 conjugacy classes of subgroups; only the 400 normal subgroups are shown.
This group has 2022 conjugacy classes of subgroups — too many to draw. Only its 400 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. C22×#14519844 | C2 | semidirect |
| 2. C2×#16840620 | C2 | direct (N × H) |
| 6. C2×#14519844 | C22 | semidirect |
| 7. #16840620 | C22 | direct (N × H) |
| 18. #14519844 | C23 | semidirect |
| 105. C22×C61 | #331 | semidirect |
| 121. C2×C61 | C2×#331 | semidirect |
| 136. C61 | C22×#331 | semidirect |
| 229. C22 | #16840620 | direct (N × H) |
| 240. C2 | C2×#16840620 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519844 | 2 |
| C2×#16840620 | 2 |
| C22×#14519773 | 2 |
| C22×#331 | 61 |