Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
306 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 2. #21462039 | C2 | semidirect |
| 4. #21461936 | C2 | semidirect |
| 5. #21460899 | C2 | semidirect |
| 6. #21460891 | C2 | semidirect |
| 23. #16839579 | C4 | semidirect |
| 24. #16839577 | C4 | semidirect |
| 25. #16839575 | C4 | semidirect |
| 26. C61×#361 | C4 | semidirect |
| 171. #361 | #6923 | semidirect |
| 177. C61 | #13156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840678 | 2 |
| #21462039 | 2 |
| #21461976 | 2 |
| #21461936 | 2 |
| #21460899 | 2 |
| #21460891 | 2 |
| #21447565 | 2 |
| #13156 | 61 |