Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
572 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 124 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. #21461536 | C2 | semidirect |
| 2. C4×#14519832 | C2 | semidirect |
| 4. #21460695 | C2 | semidirect |
| 12. #16840618 | C4 | semidirect |
| 29. #14519832 | C2×C4 | semidirect |
| 30. #14519832 | C2×C4 | semidirect |
| 207. C61 | #8226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461536 | 2 |
| C4×#14519832 | 2 |
| C2×#16840618 | 2 |
| #21460695 | 2 |
| C4×#14519766 | 2 |
| #8226 | 61 |