Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 410 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. #11763345 | C2 | semidirect |
| 2. C2×#10587622 | C2 | semidirect |
| 3. #11763190 | C2 | semidirect |
| 4. #11763162 | C2 | semidirect |
| 5. #11763029 | C2 | semidirect |
| 6. #11763023 | C2 | semidirect |
| 7. #11762964 | C2 | semidirect |
| 8. #11762950 | C2 | semidirect |
| 10. #11762859 | C2 | semidirect |
| 11. C17×#450 | C2 | semidirect |
| 18. #10587633 | C22 | semidirect |
| 19. Q8×Dic17 | C22 | semidirect |
| 20. C2×#63231 | C22 | semidirect |
| 28. C2×#63219 | C22 | semidirect |
| 30. #10587579 | C22 | semidirect |
| 32. #10587576 | C22 | semidirect |
| 39. #10587487 | C22 | semidirect |
| 40. #10587485 | C22 | semidirect |
| 41. C8×Dic17 | C22 | semidirect |
| 42. #10587481 | C22 | semidirect |
| 145. #450 | D17 | semidirect |
| 186. C17 | #3211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763345 | 2 |
| C2×#10587622 | 2 |
| #11763190 | 2 |
| #11763162 | 2 |
| #11763029 | 2 |
| #11763023 | 2 |
| #11762964 | 2 |
| #11762950 | 2 |
| #11762943 | 2 |
| #11762859 | 2 |
| C17×#450 | 2 |
| #3211 | 17 |