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. C22×#63228 | C2 | semidirect |
| 2. #11763373 | C2 | semidirect |
| 3. #11763284 | C2 | semidirect |
| 4. #11763026 | C2 | semidirect |
| 5. #11763002 | C2 | semidirect |
| 6. #11762837 | C2 | semidirect |
| 7. #11762815 | C2 | semidirect |
| 8. #11762805 | C2 | semidirect |
| 9. C2×C17×AGL(1,ℤ/8) | C2 | semidirect |
| 14. C2×SD16×C17 | C22 | semidirect |
| 15. C2×D8×C17 | C22 | semidirect |
| 18. #10587633 | C22 | semidirect |
| 19. #10587626 | C22 | semidirect |
| 22. D4×Dic17 | C22 | semidirect |
| 29. #10587506 | C22 | semidirect |
| 30. #10587503 | C22 | semidirect |
| 31. #10587492 | C22 | semidirect |
| 32. #10587485 | C22 | semidirect |
| 41. C2×D4×C17 | D4 | semidirect |
| 116. C2×AGL(1,ℤ/8) | D17 | semidirect |
| 135. C2×SD16 | C2×D17 | semidirect |
| 138. C2×D8 | C2×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 |
|---|---|
| C22×#63228 | 2 |
| #11763373 | 2 |
| #11763284 | 2 |
| #11763026 | 2 |
| #11763002 | 2 |
| #11762837 | 2 |
| #11762815 | 2 |
| #11762805 | 2 |
| C2×C17×AGL(1,ℤ/8) | 2 |
| #3041 | 17 |