Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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. #11763343 | C2 | semidirect |
| 2. C2×#10587561 | C2 | semidirect |
| 3. #11763193 | C2 | semidirect |
| 4. #11763164 | C2 | semidirect |
| 5. #11763032 | C2 | semidirect |
| 6. #11763025 | C2 | semidirect |
| 7. #11762967 | C2 | semidirect |
| 8. #11762962 | C2 | semidirect |
| 9. #11762950 | C2 | semidirect |
| 11. C17×#431 | C2 | semidirect |
| 21. C2×Dic68 | C22 | semidirect |
| 24. C2×#63219 | C22 | semidirect |
| 30. #10587561 | C22 | semidirect |
| 31. C4×D68 | C22 | semidirect |
| 33. #10587556 | C22 | semidirect |
| 34. C4×Dic34 | C22 | semidirect |
| 35. C17×C4⋊C8 | C22 | semidirect |
| 38. C4×C8×C17 | C22 | semidirect |
| 41. #10587487 | C22 | semidirect |
| 42. #10587487 | C22 | semidirect |
| 148. #431 | D17 | semidirect |
| 178. C4⋊C8 | C2×D17 | semidirect |
| 185. C4×C8 | C2×D17 | semidirect |
| 186. C17 | #3211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763343 | 2 |
| C2×#10587561 | 2 |
| #11763193 | 2 |
| #11763164 | 2 |
| #11763032 | 2 |
| #11763025 | 2 |
| #11762967 | 2 |
| #11762962 | 2 |
| #11762950 | 2 |
| #11762945 | 2 |
| C17×#431 | 2 |
| #3211 | 17 |