Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
332 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 104 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. #21462154 | C2 | semidirect |
| 4. C2×#16840648 | C2 | semidirect |
| 5. #21460873 | C2 | semidirect |
| 6. #21460864 | C2 | semidirect |
| 161. C61 | #13124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462154 | 2 |
| C2×#16840660 | 2 |
| #21462049 | 2 |
| C2×#16840648 | 2 |
| #21460873 | 2 |
| #21460864 | 2 |
| #21445659 | 2 |
| #13124 | 61 |