Order 13568.
606 conjugacy classes of subgroups.
The subgroup lattice has 410 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. #16811644 | C4 | semidirect |
| 9. #16811639 | C4 | semidirect |
| 24. #16810647 | C4 | semidirect |
| 26. M16×Dic53 | C4 | semidirect |
| 27. C53×#423 | C4 | semidirect |
| 221. #423 | #6157 | semidirect |
| 232. C53 | #8105 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291392 | 2 |
| #20291164 | 2 |
| #20289615 | 2 |
| #20283347 | 2 |
| #8105 | 53 |