Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
432 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 88 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×#63242 | C2 | semidirect |
| 2. C2×#10587547 | C2 | semidirect |
| 3. #11763751 | C2 | semidirect |
| 4. #11763682 | C2 | semidirect |
| 15. C17×#121 | C4 | semidirect |
| 17. #10587624 | C4 | semidirect |
| 18. #10587616 | C4 | semidirect |
| 19. #10587581 | C4 | semidirect |
| 55. #63242 | D4 | semidirect |
| 111. C22×C17 | #102 | semidirect |
| 122. C2×D17 | #102 | semidirect |
| 161. #121 | #595 | semidirect |
| 168. C17 | #1893 | semidirect |
| 268. C22 | #10587547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63242 | 2 |
| C2×#10587547 | 2 |
| #11763751 | 2 |
| #11763682 | 2 |
| #121×D17 | 2 |
| #1893 | 17 |