Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21458921 | C2 | semidirect |
| 3. C2×#16839573 | C2 | semidirect |
| 4. #21447546 | C2 | semidirect |
| 5. #21445875 | C2 | semidirect |
| 6. #21443919 | C2 | semidirect |
| 7. C61×#1388 | C2 | semidirect |
| 15. #16840038 | C4 | semidirect |
| 16. #16840033 | C4 | semidirect |
| 178. #1388 | D61 | semidirect |
| 205. C61 | #13070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458921 | 2 |
| #21455540 | 2 |
| C2×#16839573 | 2 |
| #21447546 | 2 |
| #21445875 | 2 |
| #21443919 | 2 |
| C61×#1388 | 2 |
| #13070 | 61 |