Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 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. #11719308 | C2 | semidirect |
| 3. #11718816 | C2 | semidirect |
| 4. D8×Dic13 | C2 | semidirect |
| 5. #11718777 | C2 | semidirect |
| 6. #11718762 | C2 | semidirect |
| 7. #11718703 | C2 | semidirect |
| 8. #11718535 | C2 | semidirect |
| 9. #11718534 | C2 | semidirect |
| 10. #11718426 | C2 | semidirect |
| 11. #11718418 | C2 | semidirect |
| 188. C13 | #3175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719308 | 2 |
| C13×#466 | 2 |
| #11718816 | 2 |
| D8×Dic13 | 2 |
| #11718777 | 2 |
| #11718762 | 2 |
| #11718703 | 2 |
| #11718535 | 2 |
| #11718534 | 2 |
| #11718426 | 2 |
| #11718418 | 2 |
| #3175 | 13 |