Order 15616.
1214 conjugacy classes of subgroups.
The subgroup lattice has 386 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #21461082 | C2 | semidirect |
| 4. #21461062 | C2 | semidirect |
| 81. C2×Q8×C61 | M16 | semidirect |
| 219. C61 | #17365 | semidirect |
| 274. C2×Q8 | #11758217 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462495 | 2 |
| #21461082 | 2 |
| #21461067 | 2 |
| #21461062 | 2 |
| C22×Q8×Dic61 | 2 |
| #17365 | 61 |