Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
586 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 139 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. #22558605 | C2 | semidirect |
| 4. #22558041 | C2 | semidirect |
| 24. #14524030 | C8 | semidirect |
| 55. C2×Dic134 | C2×C8 | semidirect |
| 72. C4×Dic67 | C2×C8 | semidirect |
| 158. C67 | #8957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569233 | 2 |
| C4×#14524030 | 2 |
| #22558605 | 2 |
| #22558041 | 2 |
| C67×#1460 | 2 |
| #8957 | 67 |