Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
318 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 36. C2×#11758185 | Q8 | semidirect |
| 52. M32×C61 | Q8 | semidirect |
| 55. #108×C61 | Q8 | semidirect |
| 158. C61 | #13455 | semidirect |
| 172. M32 | Dic122 | semidirect |
| 178. #108 | Dic122 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456355 | 2 |
| #21447607 | 2 |
| C2×#16839587 | 2 |
| #21446605 | 2 |
| #21443916 | 2 |
| #21443909 | 2 |
| C61×#1387 | 2 |
| #13455 | 61 |