Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 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×#10587573 | C2 | semidirect |
| 4. #11762715 | C2 | semidirect |
| 5. #11762703 | C2 | semidirect |
| 6. #11762681 | C2 | semidirect |
| 7. #11762678 | C2 | semidirect |
| 8. #11762655 | C2 | semidirect |
| 18. #10587622 | C4 | semidirect |
| 46. C2×Dic34 | C2×C4 | semidirect |
| 51. C22⋊Dic17 | C2×C4 | semidirect |
| 56. C4×Dic17 | C2×C4 | semidirect |
| 141. C17 | #2326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587622 | 2 |
| C2×#10587573 | 2 |
| C2×D4×Dic17 | 2 |
| #11762715 | 2 |
| #11762703 | 2 |
| #11762681 | 2 |
| #11762678 | 2 |
| #11762655 | 2 |
| C17×#390 | 2 |
| #2326 | 17 |