Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
230 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×C8×Dic17 | C2 | semidirect |
| 5. #11762573 | C2 | semidirect |
| 6. #11762568 | C2 | semidirect |
| 7. C17×#424 | C2 | semidirect |
| 19. #10587481 | C4 | semidirect |
| 20. #10587480 | C4 | semidirect |
| 86. #424 | D17 | semidirect |
| 111. C17 | #1937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587496 | 2 |
| #11762803 | 2 |
| #11762775 | 2 |
| C2×C8×Dic17 | 2 |
| #11762573 | 2 |
| #11762568 | 2 |
| C17×#424 | 2 |
| #1937 | 17 |