Order 17152.
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. #22560096 | C2 | semidirect |
| 5. #22560091 | C2 | semidirect |
| 11. #16863434 | C4 | semidirect |
| 12. #16863434 | C4 | semidirect |
| 15. C2×#14523977 | C4 | semidirect |
| 16. C2×#14523975 | C4 | semidirect |
| 19. #16863351 | C4 | semidirect |
| 26. C2×#108×C67 | C4 | semidirect |
| 51. #14523953 | C2×C4 | semidirect |
| 53. C8×Dic67 | C2×C4 | semidirect |
| 68. #108×C67 | C2×C4 | semidirect |
| 69. #108×C67 | C2×C4 | semidirect |
| 181. C67 | #20446 | semidirect |
| 187. C2×#108 | Dic67 | semidirect |
| 234. #108 | C2×Dic67 | semidirect |
| 235. #108 | C2×Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863434 | 2 |
| #22568627 | 2 |
| C2×#16863351 | 2 |
| #22560096 | 2 |
| #22560091 | 2 |
| #22559920 | 2 |
| C22×#108×C67 | 2 |
| #20446 | 67 |