Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
300 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. #11762767 | C2 | semidirect |
| 5. C2×C8×Dic17 | C2 | semidirect |
| 6. #11762570 | C2 | semidirect |
| 7. C17×#341 | C2 | semidirect |
| 16. #10587593 | C4 | semidirect |
| 19. #10587496 | C4 | semidirect |
| 20. #10587492 | C4 | semidirect |
| 21. #10587487 | C4 | semidirect |
| 99. #341 | D17 | semidirect |
| 123. C17 | #1764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587593 | 2 |
| C2×#10587496 | 2 |
| #11762806 | 2 |
| #11762767 | 2 |
| C2×C8×Dic17 | 2 |
| #11762570 | 2 |
| C17×#341 | 2 |
| #1764 | 17 |