Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
504 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10587594 | C2 | semidirect |
| 2. #11763387 | C2 | semidirect |
| 3. #11763373 | C2 | semidirect |
| 4. #11763062 | C2 | semidirect |
| 5. #11763055 | C2 | semidirect |
| 6. #11763045 | C2 | semidirect |
| 7. #11763038 | C2 | semidirect |
| 8. #11762851 | C2 | semidirect |
| 9. #11762806 | C2 | semidirect |
| 10. C2×#10587492 | C2 | semidirect |
| 11. C2×C17×#131 | C2 | semidirect |
| 17. C2×M16×C17 | C22 | semidirect |
| 19. C22×C8×C17 | C22 | semidirect |
| 28. #10587616 | C22 | semidirect |
| 31. #10587610 | C22 | semidirect |
| 37. #10587492 | C22 | semidirect |
| 38. #10587492 | C22 | semidirect |
| 39. #10587489 | C22 | semidirect |
| 40. #10587488 | C22 | semidirect |
| 41. #10587487 | C22 | semidirect |
| 42. #10587487 | C22 | semidirect |
| 66. M16×C17 | D4 | semidirect |
| 146. C2×#131 | D17 | semidirect |
| 171. C2×M16 | C2×D17 | semidirect |
| 173. C22×C8 | C2×D17 | semidirect |
| 194. C17 | #3062 | semidirect |
| 220. M16 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587594 | 2 |
| #11763387 | 2 |
| #11763373 | 2 |
| #11763062 | 2 |
| #11763055 | 2 |
| #11763045 | 2 |
| #11763038 | 2 |
| #11762851 | 2 |
| #11762806 | 2 |
| C2×#10587492 | 2 |
| C2×C17×#131 | 2 |
| #3062 | 17 |