Order 13568.
750 conjugacy classes of subgroups.
The subgroup lattice has 418 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #20289806 | C2 | direct (N × H) |
| 208. C2×C53 | #1392 | semidirect |
| 226. C53 | C2×#1392 | semidirect |
| 415. C2 | #20289806 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811609 | 2 |
| #20289806 | 2 |
| C2×#16810589 | 2 |
| C2×#1392 | 53 |