Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
2190 conjugacy classes of subgroups.
The subgroup lattice has 500 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×#16863166 | C2 | direct (N × H) |
| 12. C22×#11761612 | C4 | semidirect |
| 13. C22×#11761612 | C4 | semidirect |
| 14. C22×#11761612 | C4 | semidirect |
| 18. C23×C67⋊C8 | C4 | semidirect |
| 19. #16863166 | C22 | direct (N × H) |
| 41. C2×#11761612 | C2×C4 | semidirect |
| 42. C2×#11761612 | C2×C4 | semidirect |
| 43. C2×#11761612 | C2×C4 | semidirect |
| 51. C22×C67⋊C8 | C2×C4 | semidirect |
| 86. #11761612 | C22×C4 | semidirect |
| 92. C2×C67⋊C8 | C22×C4 | semidirect |
| 224. C22×C67 | #344 | semidirect |
| 248. C2×C67 | C2×#344 | semidirect |
| 254. C67 | C22×#344 | semidirect |
| 474. C22 | #16863166 | direct (N × H) |
| 497. C2 | C2×#16863166 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11761612 | 2 |
| C2×#16863166 | 2 |
| C22×#117×C67 | 2 |
| C22×#344 | 67 |