Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
584 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 137 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×#10587594 | C2 | semidirect |
| 2. C2×#10587618 | C2 | semidirect |
| 3. C2×#10587626 | C2 | semidirect |
| 4. #11763277 | C2 | semidirect |
| 5. #11763008 | C2 | semidirect |
| 6. #11763003 | C2 | semidirect |
| 7. #11762832 | C2 | semidirect |
| 8. #11762813 | C2 | semidirect |
| 9. C17×#418 | C2 | semidirect |
| 19. C2×#63229 | C22 | semidirect |
| 21. C2×#63228 | C22 | semidirect |
| 25. C2×D136 | C22 | semidirect |
| 26. C2×#63219 | C22 | semidirect |
| 27. #10587579 | C22 | semidirect |
| 28. #10587573 | C22 | semidirect |
| 32. C17×#102 | C22 | semidirect |
| 33. #10587485 | C22 | semidirect |
| 34. #10587480 | C22 | semidirect |
| 48. #63252 | D4 | semidirect |
| 101. D68 | C2×D4 | semidirect |
| 105. Dic34 | C2×D4 | semidirect |
| 126. Dic17 | AGL(1,ℤ/8) | semidirect |
| 135. #418 | D17 | semidirect |
| 166. #102 | C2×D17 | semidirect |
| 167. C17 | #3038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587594 | 2 |
| C2×#10587618 | 2 |
| C2×#10587626 | 2 |
| #11763277 | 2 |
| #11763008 | 2 |
| #11763003 | 2 |
| #11762832 | 2 |
| #11762813 | 2 |
| C17×#418 | 2 |
| #3038 | 17 |