Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1974 conjugacy classes of subgroups.
The subgroup lattice has 314 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21454908 | C2 | semidirect |
| 2. #21454904 | C2 | semidirect |
| 3. #21454900 | C2 | semidirect |
| 4. Q8×#11758194 | C2 | semidirect |
| 7. #16839893 | C22 | semidirect |
| 8. Q8×#92418 | C22 | semidirect |
| 67. C2×Q8×C61 | M16 | semidirect |
| 183. C61 | #60248 | semidirect |
| 224. C2×Q8 | #11758194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454908 | 2 |
| #21454904 | 2 |
| #21454900 | 2 |
| Q8×#11758194 | 2 |
| #21454452 | 2 |
| C22×C4×Q8×C61 | 2 |
| #60248 | 61 |