Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 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. C22×#63228 | C2 | semidirect |
| 2. C2×#10587634 | C2 | semidirect |
| 3. #11763373 | C2 | semidirect |
| 4. #11763060 | C2 | semidirect |
| 5. #11763043 | C2 | semidirect |
| 6. #11762845 | C2 | semidirect |
| 7. #11762814 | C2 | semidirect |
| 8. #11762813 | C2 | semidirect |
| 9. C17×#535 | C2 | semidirect |
| 15. C17×#121 | C22 | semidirect |
| 25. #10587616 | C22 | semidirect |
| 28. C2×#63223 | C22 | semidirect |
| 30. C22×#3622 | C22 | semidirect |
| 31. #10587503 | C22 | semidirect |
| 32. #10587480 | C22 | semidirect |
| 33. #10587479 | C22 | semidirect |
| 34. #10587478 | C22 | semidirect |
| 67. C2×#3622 | D4 | semidirect |
| 123. #535 | D17 | semidirect |
| 151. #121 | C2×D17 | semidirect |
| 160. C17 | #3058 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63228 | 2 |
| C2×#10587634 | 2 |
| #11763373 | 2 |
| #11763060 | 2 |
| #11763043 | 2 |
| #11762845 | 2 |
| #11762814 | 2 |
| #11762813 | 2 |
| C17×#535 | 2 |
| #3058 | 17 |