Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
426 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 426 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. #11719432 | C2 | semidirect |
| 2. #11719423 | C2 | semidirect |
| 3. C13×#486 | C2 | semidirect |
| 4. #11718748 | C2 | semidirect |
| 5. #11718733 | C2 | semidirect |
| 6. #11718447 | C2 | semidirect |
| 7. #11718421 | C2 | semidirect |
| 8. #11718420 | C2 | semidirect |
| 9. #11718417 | C2 | semidirect |
| 10. C4×D104 | C2 | semidirect |
| 11. C8×Dic26 | C2 | semidirect |
| 98. D52 | #41 | semidirect |
| 103. Dic26 | D8 | semidirect |
| 110. #486 | D13 | semidirect |
| 206. C13 | #3358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719432 | 2 |
| #11719423 | 2 |
| C13×#486 | 2 |
| #11718748 | 2 |
| #11718733 | 2 |
| #11718447 | 2 |
| #11718421 | 2 |
| #11718420 | 2 |
| #11718417 | 2 |
| C4×D104 | 2 |
| C8×Dic26 | 2 |
| #3358 | 13 |