Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
366 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 11. #16840159 | C4 | semidirect |
| 33. #14519711 | Q8 | semidirect |
| 49. #108×C61 | Q8 | semidirect |
| 143. C61 | #13272 | semidirect |
| 162. #108 | Dic122 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840159 | 2 |
| C2×#16839582 | 2 |
| #21445701 | 2 |
| #21443926 | 2 |
| #21443925 | 2 |
| #21443919 | 2 |
| C61×#1383 | 2 |
| #13272 | 61 |