Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
416 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #21446105 | C2 | semidirect |
| 5. #21443940 | C2 | semidirect |
| 6. #21443939 | C2 | semidirect |
| 7. C61×#1868 | C2 | semidirect |
| 20. #16839556 | C4 | semidirect |
| 21. #16839554 | C4 | semidirect |
| 188. #1868 | D61 | semidirect |
| 218. C61 | #12969 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454888 | 2 |
| #21447482 | 2 |
| #21446202 | 2 |
| #21446105 | 2 |
| #21443940 | 2 |
| #21443939 | 2 |
| C61×#1868 | 2 |
| #12969 | 61 |