Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
716 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 2. #22570698 | C2 | semidirect |
| 3. #22569061 | C2 | semidirect |
| 4. #22562266 | C2 | semidirect |
| 5. #22562252 | C2 | semidirect |
| 6. #22561967 | C2 | semidirect |
| 7. #22561929 | C2 | semidirect |
| 8. #22561917 | C2 | semidirect |
| 9. C22×SD32×C67 | C2 | semidirect |
| 19. #16863781 | C22 | semidirect |
| 20. #16863774 | C22 | semidirect |
| 26. Dic67⋊C16 | C22 | semidirect |
| 27. #16863201 | C22 | semidirect |
| 28. #16863200 | C22 | semidirect |
| 29. #16863198 | C22 | semidirect |
| 178. C22×SD32 | D67 | semidirect |
| 186. C67 | #33586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863832 | 2 |
| #22570698 | 2 |
| #22569061 | 2 |
| #22562266 | 2 |
| #22562252 | 2 |
| #22561967 | 2 |
| #22561929 | 2 |
| #22561917 | 2 |
| C22×SD32×C67 | 2 |
| #33586 | 67 |