Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
302 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 78 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. D61⋊M64 | C2 | semidirect |
| 2. C2×#16840689 | C2 | semidirect |
| 3. #21460973 | C2 | semidirect |
| 4. #21460972 | C2 | semidirect |
| 7. #16840695 | C22 | semidirect |
| 11. #16840689 | C22 | semidirect |
| 14. #16840194 | C4 | semidirect |
| 18. Q32×D61 | C4 | semidirect |
| 20. D16×D61 | C4 | semidirect |
| 22. C61×#508 | C4 | semidirect |
| 37. Dic488 | C2×C4 | semidirect |
| 42. D976 | C2×C4 | semidirect |
| 50. Q32×C61 | C2×C4 | semidirect |
| 52. D16×C61 | C2×C4 | semidirect |
| 142. D61 | #1418 | semidirect |
| 149. #508 | #6923 | semidirect |
| 160. C61 | C2×#1418 | semidirect |
| 175. Q32 | C2×#6923 | semidirect |
| 182. D16 | C2×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D61⋊M64 | 2 |
| C2×#16840689 | 2 |
| #21460973 | 2 |
| #21460972 | 2 |
| #508×D61 | 2 |
| C2×#1418 | 61 |