Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
358 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 119 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. #11718516 | C2 | semidirect |
| 9. #11718514 | C2 | semidirect |
| 10. #11718453 | C2 | semidirect |
| 11. #11718450 | C2 | semidirect |
| 174. C13 | #3185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719327 | 2 |
| C13×#470 | 2 |
| #11718845 | 2 |
| #11718842 | 2 |
| #11718798 | 2 |
| M16×Dic13 | 2 |
| #11718713 | 2 |
| #11718516 | 2 |
| #11718514 | 2 |
| #11718453 | 2 |
| #11718450 | 2 |
| #3185 | 13 |