Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
456 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 6. #11718377 | C2 | semidirect |
| 7. C4×Dic52 | C2 | semidirect |
| 13. C2×Dic52 | C4 | semidirect |
| 117. C13 | #2950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic52 | 2 |
| #11719221 | 2 |
| C13×#405 | 2 |
| #11718781 | 2 |
| #11718767 | 2 |
| #11718377 | 2 |
| C4×Dic52 | 2 |
| #2950 | 13 |