Order 13568.
1262 conjugacy classes of subgroups.
The subgroup lattice has 390 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 13. #16810491 | C4 | semidirect |
| 105. C42×C53 | C4⋊C4 | semidirect |
| 222. C53 | #14298 | semidirect |
| 304. C42 | #11719919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810491 | 2 |
| C2×C4×C4⋊Dic53 | 2 |
| #20272979 | 2 |
| #20272978 | 2 |
| #20272974 | 2 |
| #20272971 | 2 |
| #20272946 | 2 |
| C2×C53×#382 | 2 |
| #14298 | 53 |