Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
342 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
|---|---|---|
| 3. Q8⋊#11758187 | C2 | semidirect |
| 46. C2×Q8×C61 | C16 | semidirect |
| 135. C61 | #11637 | semidirect |
| 162. C2×Q8 | #11758187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462176 | 2 |
| Q8⋊#11758187 | 2 |
| C2×Q8×#92418 | 2 |
| #11637 | 61 |