Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
530 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #22558089 | C2 | semidirect |
| 4. #22558077 | C2 | semidirect |
| 11. #16863262 | C4 | semidirect |
| 12. #16863256 | C4 | semidirect |
| 15. C4×C4⋊Dic67 | C4 | semidirect |
| 16. C2×C67⋊#95 | C4 | semidirect |
| 195. C67 | #8760 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22563119 | 2 |
| #22560197 | 2 |
| #22558089 | 2 |
| #22558077 | 2 |
| C67×#1459 | 2 |
| #8760 | 67 |