Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
606 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 606 conjugacy classes of subgroups — too many to draw. Only its 144 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. #21461941 | C2 | semidirect |
| 2. C2×#16840625 | C2 | semidirect |
| 3. C2×#16840610 | C2 | semidirect |
| 4. C2×C8×#92420 | C2 | semidirect |
| 34. C2×D488 | C8 | semidirect |
| 69. C2×#92420 | D8 | semidirect |
| 116. C8×C61 | C22⋊C8 | semidirect |
| 164. C61 | #9657 | semidirect |
| 262. C8 | #14519834 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461941 | 2 |
| C2×#16840625 | 2 |
| C2×#16840610 | 2 |
| C2×C8×#92420 | 2 |
| C2×#16839844 | 2 |
| #9657 | 61 |