Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
292 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 88 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. #11763775 | C2 | semidirect |
| 4. #11763768 | C2 | semidirect |
| 5. #11763684 | C2 | semidirect |
| 6. #11763680 | C2 | semidirect |
| 9. #10587680 | C4 | semidirect |
| 11. #10587678 | C4 | semidirect |
| 20. #10587549 | C4 | semidirect |
| 21. #10587547 | C4 | semidirect |
| 25. C17×#104 | C4 | semidirect |
| 26. #10587508 | C4 | semidirect |
| 27. #10587496 | C4 | semidirect |
| 28. #10587476 | C4 | semidirect |
| 143. #104 | #595 | semidirect |
| 149. C17 | #1765 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D17⋊#131 | 2 |
| #11763799 | 2 |
| #11763775 | 2 |
| #11763768 | 2 |
| #11763684 | 2 |
| #11763680 | 2 |
| #104×D17 | 2 |
| #1765 | 17 |