Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
326 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 4. #11718490 | C2 | semidirect |
| 6. #11718343 | C2 | semidirect |
| 7. #11718342 | C2 | semidirect |
| 8. #11718342 | C2 | semidirect |
| 9. #11718341 | C2 | semidirect |
| 166. C13 | #3231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719175 | 2 |
| C13×#431 | 2 |
| #11718490 | 2 |
| #11718384 | 2 |
| #11718343 | 2 |
| #11718342 | 2 |
| #11718341 | 2 |
| #3231 | 13 |