Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1436 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 1436 conjugacy classes of subgroups — too many to draw. Only its 232 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×#14519865 | C2 | semidirect |
| 2. C2×#16840794 | C2 | semidirect |
| 3. #21461797 | C2 | semidirect |
| 4. #21461765 | C2 | semidirect |
| 5. #21461644 | C2 | semidirect |
| 6. #21461557 | C2 | semidirect |
| 31. C2×D61⋊C8 | D4 | semidirect |
| 172. C61 | #21444 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519865 | 2 |
| C2×#16840794 | 2 |
| #21461797 | 2 |
| #21461765 | 2 |
| #21461644 | 2 |
| #21461557 | 2 |
| #21449036 | 2 |
| #21444 | 61 |