Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
300 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 300 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 |
|---|---|---|
| 4. #11718783 | C2 | semidirect |
| 5. C2×C4×#1055 | C2 | semidirect |
| 6. #11718150 | C2 | semidirect |
| 7. #11718115 | C2 | semidirect |
| 12. #88202 | C4 | semidirect |
| 19. C13×#104 | C4 | semidirect |
| 20. #88075 | C4 | semidirect |
| 21. #88072 | C4 | semidirect |
| 112. #104 | Dic13 | semidirect |
| 153. C13 | #1764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88202 | 2 |
| C2×C13×#104 | 2 |
| #11718894 | 2 |
| #11718783 | 2 |
| C2×C4×#1055 | 2 |
| #11718150 | 2 |
| #11718115 | 2 |
| #1764 | 13 |