Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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. C2×#10587590 | C2 | semidirect |
| 3. #11763378 | C2 | semidirect |
| 4. #11763289 | C2 | semidirect |
| 5. #11763032 | C2 | semidirect |
| 6. #11763025 | C2 | semidirect |
| 7. #11763010 | C2 | semidirect |
| 8. #11763005 | C2 | semidirect |
| 9. #11762811 | C2 | semidirect |
| 10. C2×#10587492 | C2 | semidirect |
| 11. C17×#424 | C2 | semidirect |
| 20. C2×Dic68 | C22 | semidirect |
| 23. C2×D136 | C22 | semidirect |
| 25. C2×#63219 | C22 | semidirect |
| 26. C2×#63219 | C22 | semidirect |
| 35. C4×D68 | C22 | semidirect |
| 36. C4×Dic34 | C22 | semidirect |
| 37. C17×C4⋊C8 | C22 | semidirect |
| 38. C17×C4⋊C8 | C22 | semidirect |
| 41. #10587492 | C22 | semidirect |
| 42. #10587487 | C22 | semidirect |
| 51. #63252 | D4 | semidirect |
| 156. #424 | D17 | semidirect |
| 191. C4⋊C8 | C2×D17 | semidirect |
| 192. C4⋊C8 | C2×D17 | semidirect |
| 197. C17 | #3045 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587594 | 2 |
| C2×#10587590 | 2 |
| #11763378 | 2 |
| #11763289 | 2 |
| #11763032 | 2 |
| #11763025 | 2 |
| #11763010 | 2 |
| #11763005 | 2 |
| #11762811 | 2 |
| C2×#10587492 | 2 |
| C17×#424 | 2 |
| #3045 | 17 |