Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
578 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 112 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×#16840674 | C2 | semidirect |
| 3. #21461696 | C2 | semidirect |
| 4. #21460876 | C2 | semidirect |
| 17. #16839999 | C4 | semidirect |
| 18. #16839998 | C4 | semidirect |
| 21. #16839995 | C4 | semidirect |
| 24. C61×#466 | C4 | semidirect |
| 29. D61⋊C16 | D4 | semidirect |
| 170. C22×C61 | #357 | semidirect |
| 181. C2×D61 | #357 | semidirect |
| 220. #466 | #6923 | semidirect |
| 227. C61 | #13059 | semidirect |
| 386. C22 | #16840674 | 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×#16840674 | 2 |
| #21461696 | 2 |
| #21460876 | 2 |
| #466×D61 | 2 |
| #13059 | 61 |