Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1882 conjugacy classes of subgroups.
The subgroup lattice has 262 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×#11758194 | C2 | semidirect |
| 2. #21454768 | C2 | semidirect |
| 3. #21454754 | C2 | semidirect |
| 4. C2×Q8×#92418 | C2 | semidirect |
| 32. #14519784 | Q8 | direct (N × H) |
| 88. #11758194 | C2×Q8 | semidirect |
| 90. C2×#92418 | C2×Q8 | semidirect |
| 99. Q8×C61 | #131 | semidirect |
| 161. C61 | Q8×#131 | semidirect |
| 230. Q8 | #14519784 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11758194 | 2 |
| #21454768 | 2 |
| #21454754 | 2 |
| C2×Q8×#92418 | 2 |
| #21454387 | 2 |
| C4×#14519784 | 2 |
| Q8×#41×C61 | 2 |
| Q8×#131 | 61 |