Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
456 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
| 10. #16840003 | C4 | semidirect |
| 12. C2×#14519711 | C4 | semidirect |
| 167. C61 | #11706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840003 | 2 |
| #21445536 | 2 |
| #21443832 | 2 |
| C61×#2112 | 2 |
| #11706 | 61 |