Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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. #11763607 | C2 | semidirect |
| 2. C2×#10587618 | C2 | semidirect |
| 3. #11763575 | C2 | semidirect |
| 4. #11763076 | C2 | semidirect |
| 5. #11763069 | C2 | semidirect |
| 6. #11762858 | C2 | semidirect |
| 7. #11762793 | C2 | semidirect |
| 8. C2×#10587504 | C2 | semidirect |
| 9. C2×C17×AGL(1,ℤ/8) | C2 | semidirect |
| 15. C2×SD16×C17 | C22 | semidirect |
| 16. C2×D8×C17 | C22 | semidirect |
| 21. #10587628 | C22 | semidirect |
| 25. #10587618 | C22 | semidirect |
| 32. #10587587 | C22 | semidirect |
| 33. #10587507 | C22 | semidirect |
| 34. #10587504 | C22 | semidirect |
| 35. #10587504 | C22 | semidirect |
| 36. #10587490 | C22 | semidirect |
| 143. C2×AGL(1,ℤ/8) | D17 | semidirect |
| 170. C2×SD16 | C2×D17 | semidirect |
| 172. C2×D8 | C2×D17 | semidirect |
| 184. C17 | #3068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763607 | 2 |
| C2×#10587618 | 2 |
| #11763575 | 2 |
| #11763076 | 2 |
| #11763069 | 2 |
| #11762858 | 2 |
| #11762793 | 2 |
| C2×#10587504 | 2 |
| C2×C17×AGL(1,ℤ/8) | 2 |
| #3068 | 17 |