Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#10587634 | C2 | semidirect |
| 3. #11763387 | C2 | semidirect |
| 4. #11763060 | C2 | semidirect |
| 5. #11763053 | C2 | semidirect |
| 6. #11763043 | C2 | semidirect |
| 7. #11763036 | C2 | semidirect |
| 8. #11762852 | C2 | semidirect |
| 9. #11762803 | C2 | semidirect |
| 10. C2×#10587503 | C2 | semidirect |
| 11. C17×#535 | C2 | semidirect |
| 28. #10587616 | C22 | semidirect |
| 30. #10587610 | C22 | semidirect |
| 32. C2×#63223 | C22 | semidirect |
| 34. C22×#3622 | C22 | semidirect |
| 37. #10587481 | C22 | semidirect |
| 38. #10587481 | C22 | semidirect |
| 39. #10587480 | C22 | semidirect |
| 40. #10587480 | C22 | semidirect |
| 41. #10587479 | C22 | semidirect |
| 42. #10587478 | C22 | semidirect |
| 79. #63223 | D4 | semidirect |
| 148. #535 | D17 | semidirect |
| 194. C17 | #3062 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587618 | 2 |
| C2×#10587634 | 2 |
| #11763387 | 2 |
| #11763060 | 2 |
| #11763053 | 2 |
| #11763043 | 2 |
| #11763036 | 2 |
| #11762852 | 2 |
| #11762803 | 2 |
| C2×#10587503 | 2 |
| C17×#535 | 2 |
| #3062 | 17 |