Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11719418 | C2 | semidirect |
| 2. D4×Dic26 | C2 | semidirect |
| 4. #11718814 | C2 | semidirect |
| 5. #11718813 | C2 | semidirect |
| 6. #11718731 | C2 | semidirect |
| 7. C4×#6105 | C2 | semidirect |
| 8. #11718512 | C2 | semidirect |
| 9. #11718492 | C2 | semidirect |
| 10. #11718426 | C2 | semidirect |
| 11. #11718422 | C2 | semidirect |
| 198. C13 | #3373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719418 | 2 |
| D4×Dic26 | 2 |
| C13×#459 | 2 |
| #11718814 | 2 |
| #11718813 | 2 |
| #11718731 | 2 |
| C4×#6105 | 2 |
| #11718512 | 2 |
| #11718492 | 2 |
| #11718426 | 2 |
| #11718422 | 2 |
| #3373 | 13 |