Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
584 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 145 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×#10587635 | C2 | semidirect |
| 2. C2×#10587626 | C2 | semidirect |
| 3. #41×Dic17 | C2 | semidirect |
| 4. #11763007 | C2 | semidirect |
| 5. #11763002 | C2 | semidirect |
| 6. #11762832 | C2 | semidirect |
| 7. #11762815 | C2 | semidirect |
| 8. #11762814 | C2 | semidirect |
| 9. C2×C17×AGL(1,ℤ/8) | C2 | semidirect |
| 15. C2×SD16×C17 | C22 | semidirect |
| 16. C2×D8×C17 | C22 | semidirect |
| 19. Q8×Dic17 | C22 | semidirect |
| 20. C2×#63230 | C22 | semidirect |
| 25. D4×Dic17 | C22 | semidirect |
| 26. C2×#63228 | C22 | semidirect |
| 32. #10587503 | C22 | semidirect |
| 33. #10587492 | C22 | semidirect |
| 34. #10587485 | C22 | semidirect |
| 38. #41×C17 | D4 | semidirect |
| 83. Q8×C17 | C2×D4 | semidirect |
| 89. D4×C17 | C2×D4 | semidirect |
| 126. Dic17 | AGL(1,ℤ/8) | semidirect |
| 128. C2×AGL(1,ℤ/8) | D17 | semidirect |
| 149. C2×SD16 | C2×D17 | semidirect |
| 151. C2×D8 | C2×D17 | semidirect |
| 167. C17 | #3038 | semidirect |
| 171. #41 | C22⋊D17 | semidirect |
| 216. Q8 | C2×C22⋊D17 | semidirect |
| 227. D4 | C2×C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587635 | 2 |
| C2×#10587626 | 2 |
| #41×Dic17 | 2 |
| #11763007 | 2 |
| #11763002 | 2 |
| #11762832 | 2 |
| #11762815 | 2 |
| #11762814 | 2 |
| C2×C17×AGL(1,ℤ/8) | 2 |
| #3038 | 17 |