Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
336 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 336 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. #11719275 | C2 | semidirect |
| 5. #11718692 | C2 | semidirect |
| 7. #11718518 | C2 | semidirect |
| 8. #11718451 | C2 | semidirect |
| 10. #11718342 | C2 | semidirect |
| 11. C8×Dic26 | C2 | semidirect |
| 188. C13 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719275 | 2 |
| #11719247 | 2 |
| C4×C13×SD16 | 2 |
| #11718827 | 2 |
| #11718692 | 2 |
| #11718668 | 2 |
| #11718518 | 2 |
| #11718451 | 2 |
| #11718429 | 2 |
| #11718342 | 2 |
| C8×Dic26 | 2 |
| #3364 | 13 |