Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
506 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 142 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 |
|---|---|---|
| 3. #21461024 | C2 | semidirect |
| 4. #21460658 | C2 | semidirect |
| 26. C2×#11758213 | C8 | semidirect |
| 30. C2×D61⋊C8 | C8 | semidirect |
| 181. C61 | #8156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840727 | 2 |
| #21461053 | 2 |
| #21461024 | 2 |
| #21460658 | 2 |
| #21444132 | 2 |
| #8156 | 61 |