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. C2×#10587618 | C2 | semidirect |
| 3. C22×#63229 | C2 | semidirect |
| 4. #11762952 | C2 | semidirect |
| 5. #11762947 | C2 | semidirect |
| 6. #11762817 | C2 | semidirect |
| 7. #11762803 | C2 | semidirect |
| 8. #11762776 | C2 | semidirect |
| 9. C17×#535 | C2 | semidirect |
| 18. C2×#63252 | C22 | semidirect |
| 20. C22×Dic34 | C22 | semidirect |
| 33. C22⋊#3622 | C22 | semidirect |
| 34. #10587481 | C22 | semidirect |
| 35. #10587481 | C22 | semidirect |
| 36. #10587480 | C22 | semidirect |
| 60. #63252 | D4 | semidirect |
| 69. C2×Dic34 | D4 | semidirect |
| 143. #535 | D17 | semidirect |
| 182. C17 | #3010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587697 | 2 |
| C2×#10587618 | 2 |
| C22×#63229 | 2 |
| #11762952 | 2 |
| #11762947 | 2 |
| #11762817 | 2 |
| #11762803 | 2 |
| #11762776 | 2 |
| C17×#535 | 2 |
| #3010 | 17 |