Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
418 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 115 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. #21443832 | C2 | semidirect |
| 5. C22×Dic244 | C4 | semidirect |
| 9. #16840003 | C4 | semidirect |
| 12. C2×#14519711 | C4 | semidirect |
| 169. C61 | #11887 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840003 | 2 |
| #21445848 | 2 |
| #21443832 | 2 |
| C2×C61×C22⋊C16 | 2 |
| #11887 | 61 |