Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
472 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 472 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. #21462664 | C2 | semidirect |
| 2. #21461582 | C2 | semidirect |
| 3. #21461274 | C2 | semidirect |
| 4. #21461208 | C2 | semidirect |
| 5. #21460706 | C2 | semidirect |
| 6. #21460685 | C2 | semidirect |
| 25. #16840048 | C4 | semidirect |
| 26. #16840042 | C4 | semidirect |
| 27. #16839959 | C4 | semidirect |
| 32. C61×#459 | C4 | semidirect |
| 216. #459 | #6923 | semidirect |
| 235. C61 | #9162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462664 | 2 |
| #21461582 | 2 |
| #21461274 | 2 |
| #21461208 | 2 |
| #21460706 | 2 |
| #21460685 | 2 |
| #21455967 | 2 |
| #9162 | 61 |