Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
454 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 129 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×C4×D68 | C2 | semidirect |
| 3. #11763145 | C2 | semidirect |
| 4. #11763128 | C2 | semidirect |
| 5. #11763110 | C2 | semidirect |
| 6. #11763025 | C2 | semidirect |
| 7. #11762962 | C2 | semidirect |
| 9. C4×#63219 | C2 | semidirect |
| 10. C4×D136 | C2 | semidirect |
| 11. C17×#431 | C2 | semidirect |
| 24. #10587561 | C22 | semidirect |
| 29. C4×D68 | C22 | semidirect |
| 31. #10587556 | C22 | semidirect |
| 32. C4×Dic34 | C22 | semidirect |
| 33. C17×C4⋊C8 | C22 | semidirect |
| 36. C4×C8×C17 | C22 | semidirect |
| 39. #10587492 | C22 | semidirect |
| 40. #10587489 | C22 | semidirect |
| 41. #10587488 | C22 | semidirect |
| 42. #10587487 | C22 | semidirect |
| 145. #431 | D17 | semidirect |
| 175. C4⋊C8 | C2×D17 | semidirect |
| 182. C4×C8 | C2×D17 | semidirect |
| 183. C17 | #3105 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763343 | 2 |
| C2×C4×D68 | 2 |
| #11763145 | 2 |
| #11763128 | 2 |
| #11763110 | 2 |
| #11763025 | 2 |
| #11762962 | 2 |
| #11762945 | 2 |
| C4×#63219 | 2 |
| C4×D136 | 2 |
| C17×#431 | 2 |
| #3105 | 17 |