Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
230 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 75 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. #11718780 | C2 | semidirect |
| 5. C2×C4×#1055 | C2 | semidirect |
| 6. #11718150 | C2 | semidirect |
| 7. #11718115 | C2 | semidirect |
| 16. #88075 | C4 | semidirect |
| 17. #88072 | C4 | semidirect |
| 138. C13 | #1937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#104 | 2 |
| #11718895 | 2 |
| #11718894 | 2 |
| #11718780 | 2 |
| C2×C4×#1055 | 2 |
| #11718150 | 2 |
| #11718115 | 2 |
| #1937 | 13 |