Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
318 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
| 38. #14519713 | Q8 | semidirect |
| 51. M32×C61 | Q8 | semidirect |
| 158. C61 | #13456 | semidirect |
| 172. M32 | Dic122 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456359 | 2 |
| C2×#16839589 | 2 |
| #21446602 | 2 |
| #21443928 | 2 |
| #21443914 | 2 |
| #21443909 | 2 |
| C61×#2159 | 2 |
| #13456 | 61 |