Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
370 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 370 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 |
|---|---|---|
| 1. #11719305 | C2 | semidirect |
| 3. #11718816 | C2 | semidirect |
| 4. #11718813 | C2 | semidirect |
| 5. #11718798 | C2 | semidirect |
| 6. M16×Dic13 | C2 | semidirect |
| 7. #11718703 | C2 | semidirect |
| 8. #11718519 | C2 | semidirect |
| 9. #11718514 | C2 | semidirect |
| 10. #11718429 | C2 | semidirect |
| 11. #11718418 | C2 | semidirect |
| 178. C13 | #3183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719305 | 2 |
| C13×#469 | 2 |
| #11718816 | 2 |
| #11718813 | 2 |
| #11718798 | 2 |
| M16×Dic13 | 2 |
| #11718703 | 2 |
| #11718519 | 2 |
| #11718514 | 2 |
| #11718429 | 2 |
| #11718418 | 2 |
| #3183 | 13 |