Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11763320 | C2 | semidirect |
| 2. #11763144 | C2 | semidirect |
| 3. #11763130 | C2 | semidirect |
| 4. #11763127 | C2 | semidirect |
| 5. #11763043 | C2 | semidirect |
| 6. #11763036 | C2 | semidirect |
| 7. #11762960 | C2 | semidirect |
| 8. #11762952 | C2 | semidirect |
| 9. #11762943 | C2 | semidirect |
| 10. C2×C22⋊#3622 | C2 | semidirect |
| 11. C2×C17×#121 | C2 | semidirect |
| 15. C2×#63252 | C22 | semidirect |
| 23. C2×#63229 | C22 | semidirect |
| 24. C2×#63228 | C22 | semidirect |
| 26. #10587616 | C22 | semidirect |
| 30. #10587612 | C22 | semidirect |
| 32. #10587610 | C22 | semidirect |
| 33. C22×#3622 | C22 | semidirect |
| 34. #10587503 | C22 | semidirect |
| 35. #10587503 | C22 | semidirect |
| 38. C22⋊#3622 | C22 | semidirect |
| 39. #10587481 | C22 | semidirect |
| 40. #10587480 | C22 | semidirect |
| 41. #10587479 | C22 | semidirect |
| 42. #10587478 | C22 | semidirect |
| 152. C2×#121 | D17 | semidirect |
| 201. C17 | #3188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763320 | 2 |
| #11763144 | 2 |
| #11763130 | 2 |
| #11763127 | 2 |
| #11763043 | 2 |
| #11763036 | 2 |
| #11762960 | 2 |
| #11762952 | 2 |
| #11762943 | 2 |
| C2×C22⋊#3622 | 2 |
| C2×C17×#121 | 2 |
| #3188 | 17 |