Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 490 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. #11763343 | C2 | semidirect |
| 2. #11763196 | C2 | semidirect |
| 3. #11763173 | C2 | semidirect |
| 4. #11763006 | C2 | semidirect |
| 5. #11763001 | C2 | semidirect |
| 6. #11762960 | C2 | semidirect |
| 7. #11762943 | C2 | semidirect |
| 8. #11762866 | C2 | semidirect |
| 9. C2×C17×#127 | C2 | semidirect |
| 18. C2×#63229 | C22 | semidirect |
| 19. C2×#63228 | C22 | semidirect |
| 25. #10587561 | C22 | semidirect |
| 26. C4×D68 | C22 | semidirect |
| 28. #10587556 | C22 | semidirect |
| 29. C4×Dic34 | C22 | semidirect |
| 30. #10587503 | C22 | semidirect |
| 31. #10587503 | C22 | semidirect |
| 33. C4⋊#3622 | C22 | semidirect |
| 34. #10587474 | C22 | semidirect |
| 122. C2×#127 | D17 | semidirect |
| 162. C17 | #3217 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763343 | 2 |
| #11763196 | 2 |
| #11763173 | 2 |
| #11763006 | 2 |
| #11763001 | 2 |
| #11762960 | 2 |
| #11762943 | 2 |
| #11762866 | 2 |
| C2×C17×#127 | 2 |
| #3217 | 17 |