Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
464 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21446024 | C2 | semidirect |
| 3. #21446002 | C2 | semidirect |
| 5. #21443705 | C2 | semidirect |
| 6. #21443667 | C2 | semidirect |
| 22. #16839499 | C4 | semidirect |
| 23. #16839499 | C4 | semidirect |
| 24. #16839496 | C4 | semidirect |
| 25. #16839496 | C4 | semidirect |
| 248. C61 | #8874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454867 | 2 |
| #21446024 | 2 |
| #21446002 | 2 |
| #21444310 | 2 |
| #21443705 | 2 |
| #21443667 | 2 |
| C61×#1871 | 2 |
| #8874 | 61 |