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. #11763133 | C2 | semidirect |
| 3. #11763133 | C2 | semidirect |
| 4. #11763127 | C2 | semidirect |
| 5. #11763122 | C2 | semidirect |
| 6. #11762849 | C2 | semidirect |
| 7. #11762845 | C2 | semidirect |
| 8. #11762813 | C2 | semidirect |
| 9. C2×#10587480 | C2 | semidirect |
| 10. #11762776 | C2 | semidirect |
| 11. C17×#520 | C2 | semidirect |
| 18. C17×#117 | C22 | semidirect |
| 20. C2×C4⋊C4×C17 | C22 | semidirect |
| 29. C22⋊#3622 | C22 | semidirect |
| 30. C22⋊#3622 | C22 | semidirect |
| 35. #10587479 | C22 | semidirect |
| 36. #10587479 | C22 | semidirect |
| 37. #10587479 | C22 | semidirect |
| 38. #10587478 | C22 | semidirect |
| 39. #10587478 | C22 | semidirect |
| 40. #10587478 | C22 | semidirect |
| 130. #520 | D17 | semidirect |
| 160. #117 | C2×D17 | semidirect |
| 162. C2×C4⋊C4 | 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 |
| #11763133 | 2 |
| #11763127 | 2 |
| #11763122 | 2 |
| #11762849 | 2 |
| #11762845 | 2 |
| #11762813 | 2 |
| C2×#10587480 | 2 |
| #11762776 | 2 |
| C17×#520 | 2 |
| #3096 | 17 |