Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
954 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 156 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. #21460699 | C2 | semidirect |
| 5. #16840705 | C4 | semidirect |
| 7. #16840704 | C4 | semidirect |
| 12. C22×#11758194 | C4 | semidirect |
| 14. #16839725 | C4 | semidirect |
| 17. C22×M16×C61 | C4 | semidirect |
| 196. C22×M16 | #6923 | semidirect |
| 208. C61 | #8049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462263 | 2 |
| #21460699 | 2 |
| C2×#16839725 | 2 |
| #8049 | 61 |