Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
3006 conjugacy classes of subgroups.
The subgroup lattice has 330 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#16863158 | C2 | direct (N × H) |
| 8. C23×C67⋊C8 | C4 | semidirect |
| 12. C22×C4⋊Dic67 | C4 | semidirect |
| 14. #16863158 | C22 | direct (N × H) |
| 19. C22×C4⋊C4×C67 | C4 | semidirect |
| 28. C22×C67⋊C8 | C2×C4 | semidirect |
| 33. C2×C4⋊Dic67 | C2×C4 | semidirect |
| 51. C2×C4⋊C4×C67 | C2×C4 | semidirect |
| 61. C2×C67⋊C8 | C22×C4 | semidirect |
| 64. C4⋊Dic67 | C22×C4 | semidirect |
| 95. C4⋊C4×C67 | C22×C4 | semidirect |
| 134. C22×C67 | #340 | semidirect |
| 157. C2×C67 | C2×#340 | semidirect |
| 169. C67 | C22×#340 | semidirect |
| 183. C22×C4⋊C4 | Dic67 | semidirect |
| 216. C2×C4⋊C4 | C2×Dic67 | semidirect |
| 260. C4⋊C4 | C22×Dic67 | semidirect |
| 299. C22 | #16863158 | direct (N × H) |
| 321. C2 | C2×#16863158 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C67⋊C8 | 2 |
| C23×C4⋊Dic67 | 2 |
| C2×#16863158 | 2 |
| C23×C4⋊C4×C67 | 2 |
| C22×#340 | 67 |