Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
418 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 16. #500×C67 | C4 | semidirect |
| 17. #494×C67 | C4 | semidirect |
| 18. #487×C67 | C4 | semidirect |
| 137. C67 | #9763 | semidirect |
| 139. #500 | Dic67 | semidirect |
| 140. #494 | Dic67 | semidirect |
| 141. #487 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22559895 | 2 |
| #22558972 | 2 |
| #22558824 | 2 |
| #22558721 | 2 |
| C67×#3170 | 2 |
| #9763 | 67 |