Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
858 conjugacy classes of subgroups; only the 335 normal subgroups are shown.
This group has 858 conjugacy classes of subgroups — too many to draw. Only its 335 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C67⋊#338 | C4 | semidirect |
| 11. #338×C67 | C4 | semidirect |
| 83. Dic67 | #338 | direct (N × H) |
| 92. C67 | C4×#338 | semidirect |
| 100. #338 | Dic67 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×Dic67 | 2 |
| C2×C67⋊#338 | 2 |
| C2×#338×C67 | 2 |
| C4×#338 | 67 |