Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
292 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #11762764 | C2 | semidirect |
| 4. C2×#10587486 | C2 | semidirect |
| 5. #11762573 | C2 | semidirect |
| 6. #11762570 | C2 | semidirect |
| 10. C17×#131 | C4 | semidirect |
| 19. #10587508 | C4 | semidirect |
| 20. #10587506 | C4 | semidirect |
| 21. #10587503 | C4 | semidirect |
| 108. #131 | Dic17 | semidirect |
| 123. C17 | #1765 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587508 | 2 |
| #11762805 | 2 |
| #11762764 | 2 |
| C2×#10587486 | 2 |
| #11762573 | 2 |
| #11762570 | 2 |
| C2×C17×#131 | 2 |
| #1765 | 17 |