Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 2. #11763292 | C2 | semidirect |
| 3. #11763134 | C2 | semidirect |
| 4. #11763134 | C2 | semidirect |
| 5. #11763128 | C2 | semidirect |
| 6. #11763123 | C2 | semidirect |
| 7. #11762851 | C2 | semidirect |
| 8. #11762847 | C2 | semidirect |
| 9. #11762815 | C2 | semidirect |
| 10. C2×#10587492 | C2 | semidirect |
| 11. C17×#408 | C2 | semidirect |
| 26. #10587612 | C22 | semidirect |
| 28. C2×C4⋊Dic17 | C22 | semidirect |
| 29. C17×C22⋊C8 | C22 | semidirect |
| 30. C17×C22⋊C8 | C22 | semidirect |
| 35. #10587489 | C22 | semidirect |
| 36. #10587489 | C22 | semidirect |
| 37. #10587489 | C22 | semidirect |
| 38. #10587488 | C22 | semidirect |
| 39. #10587488 | C22 | semidirect |
| 40. #10587488 | C22 | semidirect |
| 139. #408 | D17 | semidirect |
| 173. C22⋊C8 | C2×D17 | semidirect |
| 174. C22⋊C8 | C2×D17 | semidirect |
| 175. C17 | #3096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763373 | 2 |
| #11763292 | 2 |
| #11763134 | 2 |
| #11763128 | 2 |
| #11763123 | 2 |
| #11762851 | 2 |
| #11762847 | 2 |
| #11762815 | 2 |
| C2×#10587492 | 2 |
| C17×#408 | 2 |
| #3096 | 17 |