Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 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×#10587618 | C2 | semidirect |
| 2. #11763355 | C2 | semidirect |
| 3. C2×D4×Dic17 | C2 | semidirect |
| 4. #11763026 | C2 | semidirect |
| 5. #11763022 | C2 | semidirect |
| 6. #11763012 | C2 | semidirect |
| 7. #11763002 | C2 | semidirect |
| 8. #11762832 | C2 | semidirect |
| 9. #11762811 | C2 | semidirect |
| 10. #11762810 | C2 | semidirect |
| 11. C2×C17×AGL(1,ℤ/8) | C2 | semidirect |
| 21. #10587633 | C22 | semidirect |
| 22. #10587630 | C22 | semidirect |
| 23. #10587626 | C22 | semidirect |
| 26. #10587622 | C22 | semidirect |
| 39. #10587506 | C22 | semidirect |
| 40. #10587503 | C22 | semidirect |
| 41. #10587492 | C22 | semidirect |
| 42. #10587487 | C22 | semidirect |
| 43. #10587485 | C22 | semidirect |
| 44. #10587485 | C22 | semidirect |
| 52. C2×D4×C17 | D4 | semidirect |
| 159. Dic17 | AGL(1,ℤ/8) | semidirect |
| 161. C2×AGL(1,ℤ/8) | D17 | semidirect |
| 211. C17 | #3036 | semidirect |
| 226. C2×D4 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587618 | 2 |
| #11763355 | 2 |
| C2×D4×Dic17 | 2 |
| #11763026 | 2 |
| #11763022 | 2 |
| #11763012 | 2 |
| #11763002 | 2 |
| #11762832 | 2 |
| #11762811 | 2 |
| #11762810 | 2 |
| C2×C17×AGL(1,ℤ/8) | 2 |
| #3036 | 17 |