Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
420 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11763414 | C2 | semidirect |
| 2. #11763378 | C2 | semidirect |
| 3. #11763198 | C2 | semidirect |
| 4. #11763186 | C2 | semidirect |
| 5. #11763174 | C2 | semidirect |
| 6. #11763164 | C2 | semidirect |
| 7. #11763025 | C2 | semidirect |
| 8. #11763005 | C2 | semidirect |
| 9. #11762956 | C2 | semidirect |
| 10. #11762945 | C2 | semidirect |
| 11. C17×#433 | C2 | semidirect |
| 18. C2×D136 | C22 | semidirect |
| 19. C2×#63219 | C22 | semidirect |
| 28. #10587560 | C22 | semidirect |
| 29. C4×D68 | C22 | semidirect |
| 30. #10587556 | C22 | semidirect |
| 31. C17×C4⋊C8 | C22 | semidirect |
| 33. C17×#97 | C22 | semidirect |
| 34. C4×C8×C17 | C22 | semidirect |
| 37. #10587492 | C22 | semidirect |
| 38. #10587487 | C22 | semidirect |
| 132. #433 | D17 | semidirect |
| 159. C4⋊C8 | C2×D17 | semidirect |
| 165. #97 | C2×D17 | semidirect |
| 166. C4×C8 | C2×D17 | semidirect |
| 167. C17 | #3220 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763414 | 2 |
| #11763378 | 2 |
| #11763198 | 2 |
| #11763186 | 2 |
| #11763174 | 2 |
| #11763164 | 2 |
| #11763025 | 2 |
| #11763005 | 2 |
| #11762956 | 2 |
| #11762945 | 2 |
| C17×#433 | 2 |
| #3220 | 17 |