Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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×#10587594 | C2 | semidirect |
| 2. C22×D136 | C2 | semidirect |
| 3. #11763378 | C2 | semidirect |
| 4. #11763283 | C2 | semidirect |
| 5. #11763025 | C2 | semidirect |
| 6. #11763005 | C2 | semidirect |
| 7. #11762815 | C2 | semidirect |
| 8. #11762806 | C2 | semidirect |
| 9. C17×#424 | C2 | semidirect |
| 20. C2×D136 | C22 | semidirect |
| 21. C2×#63219 | C22 | semidirect |
| 26. #10587561 | C22 | semidirect |
| 27. #10587560 | C22 | semidirect |
| 28. C4×D68 | C22 | semidirect |
| 29. C17×C4⋊C8 | C22 | semidirect |
| 30. #10587492 | C22 | semidirect |
| 31. #10587492 | C22 | semidirect |
| 32. #10587487 | C22 | semidirect |
| 45. C2×D68 | D4 | semidirect |
| 122. #424 | D17 | semidirect |
| 150. C4⋊C8 | C2×D17 | semidirect |
| 154. C17 | #3041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587594 | 2 |
| C22×D136 | 2 |
| #11763378 | 2 |
| #11763283 | 2 |
| #11763025 | 2 |
| #11763005 | 2 |
| #11762815 | 2 |
| #11762806 | 2 |
| C17×#424 | 2 |
| #3041 | 17 |