Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11763626 | C2 | semidirect |
| 2. #11763619 | C2 | semidirect |
| 3. #11763610 | C2 | semidirect |
| 4. #11763192 | C2 | semidirect |
| 5. #11763085 | C2 | semidirect |
| 6. #11763071 | C2 | semidirect |
| 7. #11762989 | C2 | semidirect |
| 8. #11762980 | C2 | semidirect |
| 9. #11762925 | C2 | semidirect |
| 10. #11762924 | C2 | semidirect |
| 11. C17×#472 | C2 | semidirect |
| 12. #10587697 | C22 | semidirect |
| 14. C17×AGL(1,ℤ/8) | C22 | semidirect |
| 16. C17×#131 | C22 | semidirect |
| 18. #10587622 | C22 | semidirect |
| 19. C2×#63229 | C22 | semidirect |
| 30. #10587595 | C22 | semidirect |
| 31. #10587593 | C22 | semidirect |
| 33. C2×Dic68 | C22 | semidirect |
| 37. C17×#108 | C22 | semidirect |
| 38. C17×#100 | C22 | semidirect |
| 39. #10587508 | C22 | semidirect |
| 41. #10587496 | C22 | semidirect |
| 42. #10587495 | C22 | semidirect |
| 43. #10587493 | C22 | semidirect |
| 44. C8×Dic17 | C22 | semidirect |
| 149. #472 | D17 | semidirect |
| 170. AGL(1,ℤ/8) | C2×D17 | semidirect |
| 184. #131 | C2×D17 | semidirect |
| 187. #108 | C2×D17 | semidirect |
| 192. #100 | C2×D17 | semidirect |
| 194. C17 | #3290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763626 | 2 |
| #11763619 | 2 |
| #11763610 | 2 |
| #11763192 | 2 |
| #11763085 | 2 |
| #11763071 | 2 |
| #11762989 | 2 |
| #11762980 | 2 |
| #11762925 | 2 |
| #11762924 | 2 |
| C17×#472 | 2 |
| #3290 | 17 |