Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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×#10587618 | C2 | semidirect |
| 2. #11763376 | C2 | semidirect |
| 3. #11763284 | C2 | semidirect |
| 4. #11763022 | C2 | semidirect |
| 5. #11763002 | C2 | semidirect |
| 6. #11762835 | C2 | semidirect |
| 7. #11762814 | C2 | semidirect |
| 8. #11762806 | C2 | semidirect |
| 9. C22×D8×C17 | C2 | semidirect |
| 18. #10587626 | C22 | semidirect |
| 20. #10587622 | C22 | semidirect |
| 22. D4×Dic17 | C22 | semidirect |
| 23. C2×#63229 | C22 | semidirect |
| 25. C2×#63228 | C22 | semidirect |
| 29. #10587503 | C22 | semidirect |
| 30. #10587492 | C22 | semidirect |
| 31. #10587487 | C22 | semidirect |
| 32. #10587485 | C22 | semidirect |
| 40. C2×D4×C17 | D4 | semidirect |
| 117. C22×D8 | D17 | semidirect |
| 154. C17 | #3041 | semidirect |
| 168. C2×D4 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587618 | 2 |
| #11763376 | 2 |
| #11763284 | 2 |
| #11763022 | 2 |
| #11763002 | 2 |
| #11762835 | 2 |
| #11762814 | 2 |
| #11762806 | 2 |
| C22×D8×C17 | 2 |
| #3041 | 17 |