Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
224 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 224 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 |
|---|---|---|
| 1. C2×#10587490 | C2 | semidirect |
| 5. #11762764 | C2 | semidirect |
| 6. #11762569 | C2 | semidirect |
| 7. C17×#336 | C2 | semidirect |
| 15. #10587492 | C4 | semidirect |
| 16. #10587492 | C4 | semidirect |
| 20. #10587487 | C4 | semidirect |
| 21. #10587487 | C4 | semidirect |
| 106. #336 | D17 | semidirect |
| 130. C17 | #1929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587490 | 2 |
| C2×#10587476 | 2 |
| #11762806 | 2 |
| #11762775 | 2 |
| #11762764 | 2 |
| #11762569 | 2 |
| C17×#336 | 2 |
| #1929 | 17 |