Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
316 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 34. #14519717 | Q8 | semidirect |
| 50. M32×C61 | Q8 | semidirect |
| 147. C61 | #13270 | semidirect |
| 166. M32 | Dic122 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454753 | 2 |
| #21447584 | 2 |
| #21447423 | 2 |
| #21443906 | 2 |
| #21443904 | 2 |
| #21443901 | 2 |
| C61×#1376 | 2 |
| #13270 | 61 |