Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1310 conjugacy classes of subgroups; only the 240 normal subgroups are shown.
This group has 1310 conjugacy classes of subgroups — too many to draw. Only its 240 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×#16840782 | C2 | semidirect |
| 2. #21461300 | C2 | direct (N × H) |
| 3. C2×#16840618 | C2 | semidirect |
| 6. #16840782 | C22 | semidirect |
| 9. C2×#14519832 | C22 | semidirect |
| 10. #16840618 | C22 | semidirect |
| 25. #14519832 | C23 | semidirect |
| 158. C2×C61 | #1533 | semidirect |
| 178. C61 | C2×#1533 | semidirect |
| 312. C2 | #21461300 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840782 | 2 |
| #21461300 | 2 |
| C2×#16840618 | 2 |
| C22×#14519766 | 2 |
| C2×#1533 | 61 |