Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
418 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 418 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. #11763320 | C2 | semidirect |
| 2. #11763151 | C2 | semidirect |
| 3. #11763134 | C2 | semidirect |
| 4. #11763067 | C2 | semidirect |
| 5. #11763062 | C2 | semidirect |
| 6. #11763055 | C2 | semidirect |
| 7. #11762973 | C2 | semidirect |
| 8. #11762956 | C2 | semidirect |
| 9. C17×#407 | C2 | semidirect |
| 23. C2×Dic68 | C22 | semidirect |
| 24. C2×D136 | C22 | semidirect |
| 25. C2×#63219 | C22 | semidirect |
| 28. #10587492 | C22 | semidirect |
| 29. #10587492 | C22 | semidirect |
| 30. #10587489 | C22 | semidirect |
| 31. #10587488 | C22 | semidirect |
| 32. #10587488 | C22 | semidirect |
| 33. #10587487 | C22 | semidirect |
| 34. #10587487 | C22 | semidirect |
| 122. #407 | D17 | semidirect |
| 153. C17 | #3197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763320 | 2 |
| #11763151 | 2 |
| #11763134 | 2 |
| #11763067 | 2 |
| #11763062 | 2 |
| #11763055 | 2 |
| #11762973 | 2 |
| #11762956 | 2 |
| C17×#407 | 2 |
| #3197 | 17 |