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×#10587636 | C2 | semidirect |
| 3. #11763289 | C2 | semidirect |
| 4. #11763028 | C2 | semidirect |
| 5. #11763021 | C2 | semidirect |
| 6. #11763006 | C2 | semidirect |
| 7. #11763001 | C2 | semidirect |
| 8. #11762836 | C2 | semidirect |
| 9. #11762810 | C2 | semidirect |
| 10. C2×#10587503 | C2 | semidirect |
| 11. C17×#535 | C2 | semidirect |
| 22. C2×#63231 | C22 | semidirect |
| 23. C2×#63230 | C22 | semidirect |
| 25. C2×#63229 | C22 | semidirect |
| 28. C2×#63228 | C22 | semidirect |
| 35. C4×D68 | C22 | semidirect |
| 36. C4×Dic34 | C22 | semidirect |
| 37. #10587506 | C22 | semidirect |
| 40. #10587503 | C22 | semidirect |
| 41. C4⋊#3622 | C22 | semidirect |
| 42. C4⋊#3622 | C22 | semidirect |
| 60. #63252 | D4 | semidirect |
| 150. #535 | D17 | semidirect |
| 197. C17 | #3045 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587618 | 2 |
| C2×#10587636 | 2 |
| #11763289 | 2 |
| #11763028 | 2 |
| #11763021 | 2 |
| #11763006 | 2 |
| #11763001 | 2 |
| #11762836 | 2 |
| #11762810 | 2 |
| C2×#10587503 | 2 |
| C17×#535 | 2 |
| #3045 | 17 |