Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
218 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 51. #11758202 | C16 | semidirect |
| 64. #11758187 | Q16 | semidirect |
| 120. C61 | C16×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462233 | 2 |
| Q8×#11758187 | 2 |
| #21460849 | 2 |
| #21460786 | 2 |
| Q8⋊#11758187 | 2 |
| C8×#11758187 | 2 |
| #21444623 | 2 |
| C16×Q16 | 61 |