Order 15616.
3158 conjugacy classes of subgroups.
The subgroup lattice has 360 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #21448736 | C2 | direct (N × H) |
| 11. C2×C4×Dic122 | C4 | semidirect |
| 44. C4×Dic122 | C2×C4 | semidirect |
| 105. C2×Dic122 | C4⋊C4 | semidirect |
| 154. Dic122 | C2×C4⋊C4 | semidirect |
| 183. C2×C61 | #2351 | semidirect |
| 215. C61 | C2×#2351 | semidirect |
| 353. C2 | #21448736 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic122 | 2 |
| C22×#14519742 | 2 |
| #21448736 | 2 |
| C2×#16839659 | 2 |
| C2×#16839658 | 2 |
| C2×#16839626 | 2 |
| C2×C4×C4⋊Dic61 | 2 |
| C2×#16839613 | 2 |
| C2×C61×#382 | 2 |
| C2×#2351 | 61 |