Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
308 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 75 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. #22558384 | C2 | semidirect |
| 4. #22558369 | C2 | semidirect |
| 12. #541×C67 | C4 | semidirect |
| 15. #494×C67 | C4 | semidirect |
| 16. #491×C67 | C4 | semidirect |
| 22. #433×C67 | C4 | semidirect |
| 148. C67 | #13608 | semidirect |
| 149. #541 | Dic67 | semidirect |
| 152. #494 | Dic67 | semidirect |
| 153. #491 | Dic67 | semidirect |
| 159. #433 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561898 | 2 |
| #22561884 | 2 |
| #22558384 | 2 |
| #22558369 | 2 |
| C67×#3223 | 2 |
| #13608 | 67 |