Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
508 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 100 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. C22×D61⋊C16 | C2 | semidirect |
| 2. C2×#16840677 | C2 | semidirect |
| 3. #21461699 | C2 | semidirect |
| 4. #21460880 | C2 | semidirect |
| 28. D61⋊C16 | D4 | semidirect |
| 154. C22×C61 | #359 | semidirect |
| 164. C2×D61 | #359 | semidirect |
| 205. C61 | #13063 | semidirect |
| 344. C22 | #16840677 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D61⋊C16 | 2 |
| C2×#16840677 | 2 |
| #21461699 | 2 |
| #21460880 | 2 |
| #21455402 | 2 |
| #13063 | 61 |