Order 13568.
1010 conjugacy classes of subgroups.
The subgroup lattice has 348 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #20274602 | C2 | semidirect |
| 5. #20274597 | C2 | semidirect |
| 11. #16810661 | C4 | semidirect |
| 12. #16810661 | C4 | semidirect |
| 15. C2×#13133151 | C4 | semidirect |
| 16. C2×#13133149 | C4 | semidirect |
| 19. #16810578 | C4 | semidirect |
| 26. C2×#108×C53 | C4 | semidirect |
| 51. #13133127 | C2×C4 | semidirect |
| 53. C8×Dic53 | C2×C4 | semidirect |
| 68. #108×C53 | C2×C4 | semidirect |
| 69. #108×C53 | C2×C4 | semidirect |
| 186. C2×#108 | Dic53 | semidirect |
| 202. C53 | #20446 | semidirect |
| 234. #108 | C2×Dic53 | semidirect |
| 235. #108 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810661 | 2 |
| #20283133 | 2 |
| C2×#16810578 | 2 |
| #20274602 | 2 |
| #20274597 | 2 |
| #20274426 | 2 |
| C22×#108×C53 | 2 |
| #20446 | 53 |