Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
442 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11763373 | C2 | semidirect |
| 2. #11763133 | C2 | semidirect |
| 3. #11763130 | C2 | semidirect |
| 4. #11763060 | C2 | semidirect |
| 5. #11763043 | C2 | semidirect |
| 6. #11762943 | C2 | semidirect |
| 7. #11762942 | C2 | semidirect |
| 8. #11762776 | C2 | semidirect |
| 9. C17×#535 | C2 | semidirect |
| 11. C22×D4×C17 | C22 | semidirect |
| 12. C22×D68 | C22 | semidirect |
| 16. C17×#121 | C22 | semidirect |
| 19. C17×#117 | C22 | semidirect |
| 27. #10587616 | C22 | semidirect |
| 28. #10587612 | C22 | semidirect |
| 29. C2×#63223 | C22 | semidirect |
| 30. C22×#3622 | C22 | semidirect |
| 31. #10587503 | C22 | semidirect |
| 32. #10587503 | C22 | semidirect |
| 33. C22⋊#3622 | C22 | semidirect |
| 34. C22⋊#3622 | C22 | semidirect |
| 35. #10587480 | C22 | semidirect |
| 36. #10587480 | C22 | semidirect |
| 37. #10587479 | C22 | semidirect |
| 38. #10587478 | C22 | semidirect |
| 139. #535 | D17 | semidirect |
| 156. C22×D4 | C2×D17 | semidirect |
| 168. #121 | C2×D17 | semidirect |
| 174. #117 | C2×D17 | semidirect |
| 183. C17 | #3199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763373 | 2 |
| #11763133 | 2 |
| #11763130 | 2 |
| #11763060 | 2 |
| #11763043 | 2 |
| #11762943 | 2 |
| #11762942 | 2 |
| #11762776 | 2 |
| C17×#535 | 2 |
| #3199 | 17 |