Order 13568.
850 conjugacy classes of subgroups.
The subgroup lattice has 364 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. #16810676 | C4 | semidirect |
| 13. C4×C4⋊Dic53 | C4 | semidirect |
| 17. C53×#384 | C4 | semidirect |
| 22. C4×C4⋊C4×C53 | C4 | semidirect |
| 195. #384 | Dic53 | semidirect |
| 202. C4×C4⋊C4 | Dic53 | semidirect |
| 204. C53 | #8014 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810676 | 2 |
| C2×C4×C4⋊Dic53 | 2 |
| #20272593 | 2 |
| C53×#2285 | 2 |
| #8014 | 53 |