Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
492 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 84 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. #21462047 | C2 | semidirect |
| 2. C2×#16840638 | C2 | semidirect |
| 3. #21460810 | C2 | semidirect |
| 4. #21460809 | C2 | semidirect |
| 8. #16840657 | C22 | semidirect |
| 11. #16840638 | C22 | semidirect |
| 203. C61 | #11711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462047 | 2 |
| C2×#16840638 | 2 |
| #21460810 | 2 |
| #21460809 | 2 |
| #466×D61 | 2 |
| #11711 | 61 |