Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
320 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 83 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. #11762832 | C2 | semidirect |
| 3. C2×#10587476 | C2 | semidirect |
| 4. C2×#10587508 | C2 | semidirect |
| 5. C2×#10587496 | C2 | semidirect |
| 6. #11762655 | C2 | semidirect |
| 7. C2×C17×#104 | C2 | semidirect |
| 12. #10587633 | C4 | semidirect |
| 13. #10587630 | C4 | semidirect |
| 14. #10587626 | C4 | semidirect |
| 16. #10587622 | C4 | semidirect |
| 52. C42×C17 | D4 | semidirect |
| 60. C4×Dic17 | D4 | semidirect |
| 125. C2×#104 | D17 | semidirect |
| 152. C17 | #1963 | semidirect |
| 189. C42 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763355 | 2 |
| #11762832 | 2 |
| C2×#10587476 | 2 |
| C2×#10587508 | 2 |
| C2×#10587496 | 2 |
| #11762655 | 2 |
| C2×C17×#104 | 2 |
| #1963 | 17 |