Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
548 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 238 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 |
|---|---|---|
| 1. Q8×#11758187 | C2 | semidirect |
| 2. #21462205 | C2 | semidirect |
| 3. #21462183 | C2 | semidirect |
| 4. C4×#14519852 | C2 | semidirect |
| 58. #11758187 | #41 | semidirect |
| 60. Q8×C61 | M32 | semidirect |
| 110. C61 | #33485 | semidirect |
| 152. Q8 | #14519852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11758187 | 2 |
| #21462205 | 2 |
| #21462183 | 2 |
| C4×#14519852 | 2 |
| C8×#11758226 | 2 |
| #33485 | 61 |