Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
2942 conjugacy classes of subgroups.
The subgroup lattice has 368 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #22558476 | C2 | direct (N × H) |
| 10. C22×C4⋊Dic67 | C4 | semidirect |
| 35. C2×C4⋊Dic67 | C2×C4 | semidirect |
| 175. C2×C67 | #1445 | semidirect |
| 189. C67 | C2×#1445 | semidirect |
| 358. C2 | #22558476 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4⋊Dic67 | 2 |
| C22×C67⋊#95 | 2 |
| #22558476 | 2 |
| C22×#95×C67 | 2 |
| C2×#1445 | 67 |