Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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×#10587636 | C2 | semidirect |
| 2. #11763376 | C2 | semidirect |
| 3. #11763292 | C2 | semidirect |
| 4. #11763029 | C2 | semidirect |
| 5. #11763022 | C2 | semidirect |
| 6. #11763007 | C2 | semidirect |
| 7. #11763002 | C2 | semidirect |
| 8. #11762837 | C2 | semidirect |
| 9. #11762811 | C2 | semidirect |
| 10. C2×#10587503 | C2 | semidirect |
| 11. C2×C17×AGL(1,ℤ/8) | C2 | semidirect |
| 21. Q8×Dic17 | C22 | semidirect |
| 22. C2×#63231 | C22 | semidirect |
| 23. C2×#63230 | C22 | semidirect |
| 29. D4×Dic17 | C22 | semidirect |
| 30. C2×#63229 | C22 | semidirect |
| 31. C2×#63228 | C22 | semidirect |
| 39. #10587492 | C22 | semidirect |
| 40. #10587487 | C22 | semidirect |
| 41. #10587485 | C22 | semidirect |
| 42. #10587485 | C22 | semidirect |
| 45. #41×C17 | D4 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D17 | semidirect |
| 197. C17 | #3045 | semidirect |
| 202. #41 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587636 | 2 |
| #11763376 | 2 |
| #11763292 | 2 |
| #11763029 | 2 |
| #11763022 | 2 |
| #11763007 | 2 |
| #11763002 | 2 |
| #11762837 | 2 |
| #11762811 | 2 |
| C2×#10587503 | 2 |
| C2×C17×AGL(1,ℤ/8) | 2 |
| #3045 | 17 |