Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1310 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 1310 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. C2×#16840784 | C2 | semidirect |
| 2. #21461299 | C2 | direct (N × H) |
| 3. C2×#16840618 | C2 | semidirect |
| 4. C2×#16840617 | C2 | semidirect |
| 7. #16840784 | C22 | semidirect |
| 10. C2×#14519832 | C22 | semidirect |
| 11. #16840618 | C22 | semidirect |
| 12. #16840617 | C22 | semidirect |
| 29. #14519832 | C23 | semidirect |
| 196. C2×C61 | #1533 | semidirect |
| 220. C61 | C2×#1533 | semidirect |
| 388. C2 | #21461299 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840784 | 2 |
| #21461299 | 2 |
| C2×#16840618 | 2 |
| C2×#16840617 | 2 |
| C2×#124×D61 | 2 |
| C2×#1533 | 61 |