Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10587587 | C2 | semidirect |
| 3. #11763390 | C2 | semidirect |
| 4. #11763376 | C2 | semidirect |
| 5. #11763061 | C2 | semidirect |
| 6. #11763054 | C2 | semidirect |
| 7. #11763044 | C2 | semidirect |
| 8. #11763037 | C2 | semidirect |
| 9. #11762849 | C2 | semidirect |
| 10. #11762806 | C2 | semidirect |
| 11. C2×C17×#102 | C2 | semidirect |
| 29. C2×#63218 | C22 | semidirect |
| 30. C2×C8×D17 | C22 | semidirect |
| 32. #10587583 | C22 | semidirect |
| 34. #10587581 | C22 | semidirect |
| 37. #10587492 | C22 | semidirect |
| 38. #10587492 | C22 | semidirect |
| 39. #10587487 | C22 | semidirect |
| 40. #10587487 | C22 | semidirect |
| 41. #10587479 | C22 | semidirect |
| 42. #10587478 | C22 | semidirect |
| 81. #63223 | D4 | semidirect |
| 155. C2×#102 | 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×#10587587 | 2 |
| #11763390 | 2 |
| #11763376 | 2 |
| #11763061 | 2 |
| #11763054 | 2 |
| #11763044 | 2 |
| #11763037 | 2 |
| #11762849 | 2 |
| #11762806 | 2 |
| C2×C17×#102 | 2 |
| #3062 | 17 |