Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
6494 conjugacy classes of subgroups; only the 675 normal subgroups are shown.
This group has 6494 conjugacy classes of subgroups — too many to draw. Only its 675 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 |
|---|---|---|
| 2. C2×#16863268 | C2 | semidirect |
| 4. #22558431 | C2 | semidirect |
| 9. C22×Dic67⋊C4 | C22 | semidirect |
| 12. #16863252 | C4 | semidirect |
| 13. C2×C67⋊#95 | C22 | semidirect |
| 29. C2×C22⋊Dic67 | C2×C4 | semidirect |
| 52. C22×Dic67 | C22×C4 | semidirect |
| 64. C24×C67 | C4⋊C4 | semidirect |
| 119. C22×C67 | #385 | semidirect |
| 143. C67 | #14693 | semidirect |
| 189. C24 | Dic67⋊C4 | semidirect |
| 257. C22 | #16863268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×Dic67 | 2 |
| C2×#16863268 | 2 |
| C2×#16863252 | 2 |
| #22558431 | 2 |
| C2×#379×C67 | 2 |
| #14693 | 67 |