Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
488 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 123 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. #11763180 | C2 | semidirect |
| 4. #11763154 | C2 | semidirect |
| 5. #11763008 | C2 | semidirect |
| 6. #11763007 | C2 | semidirect |
| 7. #11762962 | C2 | semidirect |
| 8. #11762960 | C2 | semidirect |
| 9. #11762959 | C2 | semidirect |
| 10. #11762859 | C2 | semidirect |
| 11. C17×#450 | C2 | semidirect |
| 16. C2×SD16×C17 | C22 | semidirect |
| 18. Q8×Dic17 | C22 | semidirect |
| 19. #10587630 | C22 | semidirect |
| 20. C2×#63230 | C22 | semidirect |
| 25. C2×#63229 | C22 | semidirect |
| 28. C2×#63219 | C22 | semidirect |
| 30. #10587574 | C22 | semidirect |
| 32. #10587573 | C22 | semidirect |
| 35. C17×#102 | C22 | semidirect |
| 37. #10587503 | C22 | semidirect |
| 39. #10587492 | C22 | semidirect |
| 40. #10587485 | C22 | semidirect |
| 41. C8×Dic17 | C22 | semidirect |
| 42. #10587480 | C22 | semidirect |
| 111. C2×Dic17 | SD16 | semidirect |
| 155. #450 | D17 | semidirect |
| 170. C2×SD16 | C2×D17 | semidirect |
| 190. #102 | C2×D17 | semidirect |
| 194. C17 | #3208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763361 | 2 |
| C2×#10587626 | 2 |
| #11763180 | 2 |
| #11763154 | 2 |
| #11763008 | 2 |
| #11763007 | 2 |
| #11762962 | 2 |
| #11762960 | 2 |
| #11762959 | 2 |
| #11762859 | 2 |
| C17×#450 | 2 |
| #3208 | 17 |