Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
456 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 90 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. #21462787 | C2 | semidirect |
| 2. C2×#16840678 | C2 | semidirect |
| 3. #21462134 | C2 | semidirect |
| 4. #21461707 | C2 | semidirect |
| 5. #21460896 | C2 | semidirect |
| 6. #21460885 | C2 | semidirect |
| 25. #16840038 | C4 | semidirect |
| 26. #16840037 | C4 | semidirect |
| 27. #16840029 | C4 | semidirect |
| 32. C61×#472 | C4 | semidirect |
| 240. #472 | #6923 | semidirect |
| 252. C61 | #13070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462787 | 2 |
| C2×#16840678 | 2 |
| #21462134 | 2 |
| #21461707 | 2 |
| #21460896 | 2 |
| #21460885 | 2 |
| #21455537 | 2 |
| #13070 | 61 |