Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
364 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22558197 | C2 | semidirect |
| 11. C22×Q16×C67 | C4 | semidirect |
| 14. #470×C67 | C4 | semidirect |
| 18. #427×C67 | C4 | semidirect |
| 148. C67 | #11869 | semidirect |
| 149. C22×Q16 | Dic67 | semidirect |
| 153. #470 | Dic67 | semidirect |
| 158. #427 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561830 | 2 |
| #22560255 | 2 |
| #22558197 | 2 |
| C67×#3059 | 2 |
| #11869 | 67 |