Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
452 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 452 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 |
|---|---|---|
| 3. #21461277 | C2 | semidirect |
| 4. #21461213 | C2 | semidirect |
| 5. #21460706 | C2 | semidirect |
| 6. #21460685 | C2 | semidirect |
| 25. #16840049 | C4 | semidirect |
| 26. #16839972 | C4 | semidirect |
| 27. #16839968 | C4 | semidirect |
| 32. C61×#477 | C4 | semidirect |
| 205. #477 | #6923 | semidirect |
| 227. C61 | #9159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462661 | 2 |
| #21461583 | 2 |
| #21461277 | 2 |
| #21461213 | 2 |
| #21460706 | 2 |
| #21460685 | 2 |
| #21455984 | 2 |
| #9159 | 61 |