Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
392 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 123 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. #11719427 | C2 | semidirect |
| 3. C13×#486 | C2 | semidirect |
| 4. #11718745 | C2 | semidirect |
| 5. #11718736 | C2 | semidirect |
| 6. #11718423 | C2 | semidirect |
| 7. #11718422 | C2 | semidirect |
| 8. #11718421 | C2 | semidirect |
| 9. #11718419 | C2 | semidirect |
| 10. C4×#6095 | C2 | semidirect |
| 11. C8×Dic26 | C2 | semidirect |
| 99. Dic26 | SD16 | semidirect |
| 100. Dic26 | #41 | semidirect |
| 107. #486 | D13 | semidirect |
| 199. C13 | #3362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719427 | 2 |
| #11719423 | 2 |
| C13×#486 | 2 |
| #11718745 | 2 |
| #11718736 | 2 |
| #11718423 | 2 |
| #11718422 | 2 |
| #11718421 | 2 |
| #11718419 | 2 |
| C4×#6095 | 2 |
| C8×Dic26 | 2 |
| #3362 | 13 |