Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
740 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 2. C2×D4×Dic17 | C2 | semidirect |
| 3. C2×#10587579 | C2 | semidirect |
| 4. #11762711 | C2 | semidirect |
| 5. #11762686 | C2 | semidirect |
| 6. #11762685 | C2 | semidirect |
| 7. #11762674 | C2 | semidirect |
| 8. #11762655 | C2 | semidirect |
| 9. C17×#390 | C2 | semidirect |
| 19. #10587626 | C4 | semidirect |
| 34. C2×D4×C17 | C2×C4 | semidirect |
| 40. C2×C22⋊D17 | C2×C4 | semidirect |
| 49. C2×D68 | C2×C4 | semidirect |
| 59. C4×Dic17 | C2×C4 | semidirect |
| 60. C4×Dic17 | D4 | semidirect |
| 121. #390 | D17 | semidirect |
| 153. C17 | #2328 | semidirect |
| 164. C2×D4 | C4×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587626 | 2 |
| C2×D4×Dic17 | 2 |
| C2×#10587579 | 2 |
| #11762711 | 2 |
| #11762686 | 2 |
| #11762685 | 2 |
| #11762674 | 2 |
| #11762655 | 2 |
| C17×#390 | 2 |
| #2328 | 17 |