Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
748 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 748 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 |
|---|---|---|
| 1. C2×#16863832 | C2 | semidirect |
| 2. #22570690 | C2 | semidirect |
| 3. #22569061 | C2 | semidirect |
| 4. #22562262 | C2 | semidirect |
| 5. #22562242 | C2 | semidirect |
| 6. #22561967 | C2 | semidirect |
| 7. #22561925 | C2 | semidirect |
| 8. #22561917 | C2 | semidirect |
| 9. C22×D16×C67 | C2 | semidirect |
| 15. C2×#14523987 | C22 | semidirect |
| 16. C2×#14523984 | C22 | semidirect |
| 19. #16863779 | C22 | semidirect |
| 20. #16863771 | C22 | semidirect |
| 22. D8×Dic67 | C22 | semidirect |
| 26. Dic67⋊C16 | C22 | semidirect |
| 27. #16863201 | C22 | semidirect |
| 28. #16863198 | C22 | semidirect |
| 29. #16863197 | C22 | semidirect |
| 70. C2×D8×C67 | D4 | semidirect |
| 183. C22×D16 | D67 | semidirect |
| 191. C67 | #33585 | semidirect |
| 233. C2×D8 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863832 | 2 |
| #22570690 | 2 |
| #22569061 | 2 |
| #22562262 | 2 |
| #22562242 | 2 |
| #22561967 | 2 |
| #22561925 | 2 |
| #22561917 | 2 |
| C22×D16×C67 | 2 |
| #33585 | 67 |