Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#10587635 | C2 | semidirect |
| 2. C2×#10587634 | C2 | semidirect |
| 3. #11763373 | C2 | semidirect |
| 4. #11763060 | C2 | semidirect |
| 5. #11763057 | C2 | semidirect |
| 6. #11763043 | C2 | semidirect |
| 7. #11763040 | C2 | semidirect |
| 8. #11762849 | C2 | semidirect |
| 9. #11762805 | C2 | semidirect |
| 10. C2×#10587480 | C2 | semidirect |
| 11. C17×#537 | C2 | semidirect |
| 16. C17×C22⋊Q8 | C22 | semidirect |
| 19. C17×#121 | C22 | semidirect |
| 32. C2×#63223 | C22 | semidirect |
| 34. C22×#3622 | C22 | semidirect |
| 35. #10587506 | C22 | semidirect |
| 36. #10587506 | C22 | semidirect |
| 37. #10587503 | C22 | semidirect |
| 38. #10587503 | C22 | semidirect |
| 41. #10587479 | C22 | semidirect |
| 42. #10587478 | C22 | semidirect |
| 79. #63223 | D4 | semidirect |
| 147. #537 | D17 | semidirect |
| 177. C22⋊Q8 | C2×D17 | semidirect |
| 182. #121 | C2×D17 | semidirect |
| 194. C17 | #3062 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587635 | 2 |
| C2×#10587634 | 2 |
| #11763373 | 2 |
| #11763060 | 2 |
| #11763057 | 2 |
| #11763043 | 2 |
| #11763040 | 2 |
| #11762849 | 2 |
| #11762805 | 2 |
| C2×#10587480 | 2 |
| C17×#537 | 2 |
| #3062 | 17 |