Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
776 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 776 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #21443841 | C2 | direct (N × H) |
| 5. C23×Dic122 | C4 | semidirect |
| 10. #16839674 | C4 | semidirect |
| 13. C2×#14519684 | C4 | semidirect |
| 24. C22×Dic122 | C2×C4 | semidirect |
| 38. #14519684 | C2×C4 | semidirect |
| 207. C2×C61 | #1351 | semidirect |
| 226. C61 | C2×#1351 | semidirect |
| 409. C2 | #21443841 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839674 | 2 |
| C2×#16839529 | 2 |
| #21443841 | 2 |
| C2×C61×#323 | 2 |
| C2×#1351 | 61 |