Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
358 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 96 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. #21462166 | C2 | semidirect |
| 4. #21460881 | C2 | semidirect |
| 17. C2×#14519717 | C4 | semidirect |
| 18. C2×#14519716 | C4 | semidirect |
| 20. C2×C16×D61 | C4 | semidirect |
| 22. C22×C16×C61 | C4 | semidirect |
| 144. C22×C16 | #6923 | semidirect |
| 153. C61 | #12832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462166 | 2 |
| #21461703 | 2 |
| #21461701 | 2 |
| #21460881 | 2 |
| C2×#16840178 | 2 |
| #12832 | 61 |