Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10587697 | C2 | semidirect |
| 2. C22×#63229 | C2 | semidirect |
| 3. #11763376 | C2 | semidirect |
| 4. #11762951 | C2 | semidirect |
| 5. #11762946 | C2 | semidirect |
| 6. #11762819 | C2 | semidirect |
| 7. #11762805 | C2 | semidirect |
| 8. #11762777 | C2 | semidirect |
| 9. C2×C17×AGL(1,ℤ/8) | C2 | semidirect |
| 14. C2×Q8×D17 | C22 | semidirect |
| 16. C2×#63254 | C22 | semidirect |
| 33. #10587506 | C22 | semidirect |
| 34. #10587503 | C22 | semidirect |
| 35. #10587491 | C22 | semidirect |
| 36. #10587487 | C22 | semidirect |
| 39. #41×C17 | D4 | semidirect |
| 70. C2×Dic34 | D4 | semidirect |
| 141. C2×AGL(1,ℤ/8) | D17 | semidirect |
| 182. C17 | #3010 | semidirect |
| 191. #41 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587697 | 2 |
| C22×#63229 | 2 |
| #11763376 | 2 |
| #11762951 | 2 |
| #11762946 | 2 |
| #11762819 | 2 |
| #11762805 | 2 |
| #11762777 | 2 |
| C2×C17×AGL(1,ℤ/8) | 2 |
| #3010 | 17 |