Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
472 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22558087 | C2 | semidirect |
| 4. #22558076 | C2 | semidirect |
| 10. #16863264 | C4 | semidirect |
| 11. #16863259 | C4 | semidirect |
| 14. C4×C22⋊Dic67 | C4 | semidirect |
| 15. #16863242 | C4 | semidirect |
| 187. C67 | #8762 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22563149 | 2 |
| #22558527 | 2 |
| #22558087 | 2 |
| #22558076 | 2 |
| C67×#1799 | 2 |
| #8762 | 67 |