Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
368 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 149 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. #11718360 | C2 | semidirect |
| 5. C4×Dic52 | C2 | semidirect |
| 6. #11718343 | C2 | semidirect |
| 7. #11718342 | C2 | semidirect |
| 49. C2×C4×C13 | Q16 | semidirect |
| 122. C13 | #3170 | semidirect |
| 130. C2×C4 | Dic52 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719175 | 2 |
| C2×C4×C8×C13 | 2 |
| #11718777 | 2 |
| #11718360 | 2 |
| C4×Dic52 | 2 |
| #11718343 | 2 |
| #11718342 | 2 |
| #3170 | 13 |