Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
454 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 1. #22561894 | C2 | semidirect |
| 2. #22561874 | C2 | semidirect |
| 3. #22558366 | C2 | semidirect |
| 8. #16863193 | C22 | semidirect |
| 9. #16863191 | C22 | semidirect |
| 14. C2×#127×C67 | C4 | semidirect |
| 15. #496×C67 | C4 | semidirect |
| 19. C4×M16×C67 | C4 | semidirect |
| 161. C67 | #13579 | semidirect |
| 165. C2×#127 | Dic67 | semidirect |
| 166. #496 | Dic67 | semidirect |
| 172. C4×M16 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561894 | 2 |
| #22561874 | 2 |
| #22558366 | 2 |
| C67×#3151 | 2 |
| #13579 | 67 |