Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
292 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 113 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. #11762764 | C2 | semidirect |
| 5. #11762574 | C2 | semidirect |
| 6. #11762569 | C2 | semidirect |
| 7. C2×C17×#97 | C2 | semidirect |
| 16. #10587587 | C4 | semidirect |
| 20. #10587492 | C4 | semidirect |
| 21. #10587487 | C4 | semidirect |
| 24. #10587476 | C4 | semidirect |
| 98. C2×#97 | D17 | 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×#10587587 | 2 |
| C2×#10587476 | 2 |
| #11762806 | 2 |
| #11762764 | 2 |
| #11762574 | 2 |
| #11762569 | 2 |
| C2×C17×#97 | 2 |
| #1765 | 17 |