Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1174 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 1174 conjugacy classes of subgroups — too many to draw. Only its 280 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×D61⋊C16 | C2 | semidirect |
| 2. C22×#14519848 | C2 | semidirect |
| 3. C2×#16840676 | C2 | direct (N × H) |
| 7. C2×D61⋊C16 | C22 | semidirect |
| 10. C2×#14519848 | C22 | semidirect |
| 11. #16840676 | C22 | direct (N × H) |
| 25. D61⋊C16 | C23 | semidirect |
| 28. #14519848 | C23 | semidirect |
| 128. C22×C61 | #359 | semidirect |
| 144. C2×C61 | C2×#359 | semidirect |
| 164. C61 | C22×#359 | semidirect |
| 275. C22 | #16840676 | direct (N × H) |
| 285. C2 | C2×#16840676 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D61⋊C16 | 2 |
| C22×#14519848 | 2 |
| C2×#16840676 | 2 |
| C22×#14519796 | 2 |
| C22×#359 | 61 |