Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
380 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 82 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. C2×#16840690 | C2 | semidirect |
| 4. #21461939 | C2 | semidirect |
| 5. #21460898 | C2 | semidirect |
| 6. #21460872 | C2 | semidirect |
| 25. #16839570 | C4 | semidirect |
| 26. #16839569 | C4 | semidirect |
| 27. #16839568 | C4 | semidirect |
| 28. C61×#359 | C4 | semidirect |
| 202. #359 | #6923 | semidirect |
| 204. C61 | #12947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462596 | 2 |
| C2×#16840690 | 2 |
| #21462133 | 2 |
| #21461939 | 2 |
| #21460898 | 2 |
| #21460872 | 2 |
| #359×D61 | 2 |
| #12947 | 61 |