Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 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. #11763340 | C2 | semidirect |
| 2. C2×#10587622 | C2 | semidirect |
| 3. #11763192 | C2 | semidirect |
| 4. #11763162 | C2 | semidirect |
| 5. #11763030 | C2 | semidirect |
| 6. #11763022 | C2 | semidirect |
| 7. #11762967 | C2 | semidirect |
| 8. #11762960 | C2 | semidirect |
| 9. #11762947 | C2 | semidirect |
| 10. #11762859 | C2 | semidirect |
| 22. #10587622 | C22 | semidirect |
| 25. D4×Dic17 | C22 | semidirect |
| 27. C2×#63229 | C22 | semidirect |
| 30. C2×Dic68 | C22 | semidirect |
| 31. #10587576 | C22 | semidirect |
| 32. #10587573 | C22 | semidirect |
| 39. #10587487 | C22 | semidirect |
| 40. #10587485 | C22 | semidirect |
| 41. C8×Dic17 | C22 | semidirect |
| 42. #10587481 | C22 | semidirect |
| 186. C17 | #3211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763340 | 2 |
| C2×#10587622 | 2 |
| #11763192 | 2 |
| #11763162 | 2 |
| #11763030 | 2 |
| #11763022 | 2 |
| #11762967 | 2 |
| #11762960 | 2 |
| #11762947 | 2 |
| #11762859 | 2 |
| C17×#447 | 2 |
| #3211 | 17 |