Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 115 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. #11718845 | C2 | semidirect |
| 4. #11718842 | C2 | semidirect |
| 8. #11718519 | C2 | semidirect |
| 9. #11718514 | C2 | semidirect |
| 10. #11718458 | C2 | semidirect |
| 11. #11718451 | C2 | semidirect |
| 172. C13 | #3177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719330 | 2 |
| C13×#470 | 2 |
| #11718845 | 2 |
| #11718842 | 2 |
| #11718798 | 2 |
| #11718783 | 2 |
| #11718712 | 2 |
| #11718519 | 2 |
| #11718514 | 2 |
| #11718458 | 2 |
| #11718451 | 2 |
| #3177 | 13 |