Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
444 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 133 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. #11763366 | C2 | semidirect |
| 2. #11763144 | C2 | semidirect |
| 3. #11763089 | C2 | semidirect |
| 4. #11763014 | C2 | semidirect |
| 6. #11762909 | C2 | semidirect |
| 7. #11762866 | C2 | semidirect |
| 23. #10587555 | C22 | semidirect |
| 24. #10587555 | C22 | semidirect |
| 26. C4×Dic34 | C22 | semidirect |
| 29. #10587481 | C22 | semidirect |
| 30. #10587478 | C22 | semidirect |
| 31. C4⋊#3622 | C22 | semidirect |
| 32. #10587474 | C22 | semidirect |
| 145. C17 | #3110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763366 | 2 |
| #11763144 | 2 |
| #11763089 | 2 |
| #11763014 | 2 |
| #11762960 | 2 |
| #11762909 | 2 |
| #11762866 | 2 |
| C2×C4×D4×C17 | 2 |
| #3110 | 17 |