Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
418 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 418 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. #11719290 | C2 | semidirect |
| 2. #11719258 | C2 | semidirect |
| 3. C4×C13×SD16 | C2 | semidirect |
| 4. #11718837 | C2 | semidirect |
| 5. #11718688 | C2 | semidirect |
| 6. #11718676 | C2 | semidirect |
| 7. #11718530 | C2 | semidirect |
| 8. #11718480 | C2 | semidirect |
| 9. #11718447 | C2 | semidirect |
| 10. #11718356 | C2 | semidirect |
| 11. #11718340 | C2 | semidirect |
| 108. C8×C13 | #41 | semidirect |
| 120. C4×SD16 | D13 | semidirect |
| 211. C13 | #3399 | semidirect |
| 243. C8 | #6127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719290 | 2 |
| #11719258 | 2 |
| C4×C13×SD16 | 2 |
| #11718837 | 2 |
| #11718688 | 2 |
| #11718676 | 2 |
| #11718530 | 2 |
| #11718480 | 2 |
| #11718447 | 2 |
| #11718356 | 2 |
| #11718340 | 2 |
| #3399 | 13 |