Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
400 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 113 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. #11763361 | C2 | semidirect |
| 3. #11763200 | C2 | semidirect |
| 4. #11763167 | C2 | semidirect |
| 5. #11763030 | C2 | semidirect |
| 6. #11763029 | C2 | semidirect |
| 7. #11762967 | C2 | semidirect |
| 8. #11762964 | C2 | semidirect |
| 10. #11762863 | C2 | semidirect |
| 18. Q8×Dic17 | C22 | semidirect |
| 19. #10587630 | C22 | semidirect |
| 20. C2×#63231 | C22 | semidirect |
| 28. C2×Dic68 | C22 | semidirect |
| 30. #10587574 | C22 | semidirect |
| 32. #10587573 | C22 | semidirect |
| 39. #10587487 | C22 | semidirect |
| 40. #10587486 | C22 | semidirect |
| 41. #10587485 | C22 | semidirect |
| 42. #10587481 | C22 | semidirect |
| 182. C17 | #3215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763361 | 2 |
| C2×#10587622 | 2 |
| #11763200 | 2 |
| #11763167 | 2 |
| #11763030 | 2 |
| #11763029 | 2 |
| #11762967 | 2 |
| #11762964 | 2 |
| #11762960 | 2 |
| #11762863 | 2 |
| C17×#450 | 2 |
| #3215 | 17 |