Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
390 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. #11719175 | C2 | semidirect |
| 3. #11718900 | C2 | semidirect |
| 4. #11718751 | C2 | semidirect |
| 5. #11718736 | C2 | semidirect |
| 6. #11718721 | C2 | semidirect |
| 7. #11718716 | C2 | semidirect |
| 8. #11718587 | C2 | semidirect |
| 173. C13 | #3216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#532 | 2 |
| #11719175 | 2 |
| #11718900 | 2 |
| #11718751 | 2 |
| #11718736 | 2 |
| #11718721 | 2 |
| #11718716 | 2 |
| #11718587 | 2 |
| #3216 | 13 |