Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 125 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×#10587560 | C2 | semidirect |
| 2. #11763343 | C2 | semidirect |
| 3. #11763198 | C2 | semidirect |
| 4. #11763174 | C2 | semidirect |
| 5. #11763010 | C2 | semidirect |
| 6. #11763005 | C2 | semidirect |
| 7. #11762962 | C2 | semidirect |
| 8. #11762945 | C2 | semidirect |
| 9. C17×#432 | C2 | semidirect |
| 18. C2×D136 | C22 | semidirect |
| 19. C2×#63219 | C22 | semidirect |
| 21. #10587561 | C22 | semidirect |
| 26. C4×D68 | C22 | semidirect |
| 28. #10587556 | C22 | semidirect |
| 29. C4×Dic34 | C22 | semidirect |
| 30. C17×C4⋊C8 | C22 | semidirect |
| 32. C17×#97 | C22 | semidirect |
| 33. #10587492 | C22 | semidirect |
| 34. #10587492 | C22 | semidirect |
| 130. #432 | D17 | semidirect |
| 157. C4⋊C8 | C2×D17 | semidirect |
| 161. #97 | C2×D17 | semidirect |
| 162. C17 | #3217 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587560 | 2 |
| #11763343 | 2 |
| #11763198 | 2 |
| #11763174 | 2 |
| #11763010 | 2 |
| #11763005 | 2 |
| #11762962 | 2 |
| #11762945 | 2 |
| C17×#432 | 2 |
| #3217 | 17 |