Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
438 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 76 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. #21462644 | C2 | semidirect |
| 2. #21461295 | C2 | semidirect |
| 3. C2×#16840618 | C2 | semidirect |
| 4. #21461090 | C2 | semidirect |
| 5. #21460714 | C2 | semidirect |
| 6. #21460658 | C2 | semidirect |
| 247. C61 | #9265 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462644 | 2 |
| #21461295 | 2 |
| C2×#16840618 | 2 |
| #21461090 | 2 |
| #21460714 | 2 |
| #21460658 | 2 |
| #21456783 | 2 |
| #9265 | 61 |