Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
2886 conjugacy classes of subgroups.
The subgroup lattice has 442 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C2×C67⋊#95 | C4 | semidirect |
| 14. C22×C4⋊C4×C67 | C4 | semidirect |
| 67. C22×Dic67 | C4⋊C4 | semidirect |
| 156. C2×C4×C67 | #95 | semidirect |
| 224. C67 | #7557 | semidirect |
| 230. C22×C4⋊C4 | Dic67 | semidirect |
| 388. C2×C4 | C67⋊#95 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C67⋊#95 | 2 |
| C23×C4⋊C4×C67 | 2 |
| #7557 | 67 |