Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
414 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 115 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×#16839582 | C2 | semidirect |
| 5. #21445982 | C2 | semidirect |
| 6. #21443929 | C2 | semidirect |
| 7. C61×#1387 | C2 | semidirect |
| 12. #16839878 | C4 | semidirect |
| 157. #1387 | D61 | semidirect |
| 182. C61 | #12820 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839878 | 2 |
| C2×#16839582 | 2 |
| #21447532 | 2 |
| #21447529 | 2 |
| #21445982 | 2 |
| #21443929 | 2 |
| C61×#1387 | 2 |
| #12820 | 61 |