Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 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. #11763359 | C2 | semidirect |
| 2. C2×#10587561 | C2 | semidirect |
| 3. #11763198 | C2 | semidirect |
| 4. #11763169 | C2 | semidirect |
| 5. #11763025 | C2 | semidirect |
| 6. #11762950 | C2 | semidirect |
| 7. #11762945 | C2 | semidirect |
| 8. C17×#432 | C2 | semidirect |
| 18. C2×#63219 | C22 | semidirect |
| 24. #10587560 | C22 | semidirect |
| 26. C4×D68 | C22 | semidirect |
| 27. #10587555 | C22 | semidirect |
| 28. C17×C4⋊C8 | C22 | semidirect |
| 30. C17×#97 | C22 | semidirect |
| 32. #10587487 | C22 | semidirect |
| 122. #432 | D17 | semidirect |
| 148. C4⋊C8 | C2×D17 | semidirect |
| 152. #97 | C2×D17 | semidirect |
| 153. C17 | #3213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763359 | 2 |
| C2×#10587561 | 2 |
| #11763198 | 2 |
| #11763169 | 2 |
| #11763025 | 2 |
| #11762950 | 2 |
| #11762945 | 2 |
| C17×#432 | 2 |
| #3213 | 17 |