Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
548 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 86 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. #21461699 | C2 | semidirect |
| 2. C8×C22⋊#6923 | C2 | semidirect |
| 3. #21461215 | C2 | semidirect |
| 4. #21461094 | C2 | semidirect |
| 21. C2×#14519711 | C4 | semidirect |
| 22. C2×#14519698 | C4 | semidirect |
| 23. C22×D8×C61 | C4 | semidirect |
| 176. C22×D8 | #6923 | semidirect |
| 194. C61 | #9815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461699 | 2 |
| C8×C22⋊#6923 | 2 |
| #21461215 | 2 |
| #21461094 | 2 |
| C2×#16839995 | 2 |
| #9815 | 61 |