Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
506 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 160 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 |
|---|---|---|
| 2. #21461022 | C2 | semidirect |
| 3. #21460659 | C2 | semidirect |
| 25. C2×#11758189 | C8 | semidirect |
| 31. C2×C8×D61 | C8 | semidirect |
| 147. C61 | #8156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461052 | 2 |
| #21461022 | 2 |
| #21460659 | 2 |
| C2×#16839719 | 2 |
| #8156 | 61 |