Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
390 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 91 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. C22×Dic52 | C2 | semidirect |
| 5. C2×#88056 | C2 | semidirect |
| 6. #11718590 | C2 | semidirect |
| 7. C13×#336 | C2 | semidirect |
| 108. #336 | D13 | semidirect |
| 189. C13 | #2015 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic52 | 2 |
| C22×#6095 | 2 |
| C2×#88129 | 2 |
| C2×#88061 | 2 |
| C2×#88056 | 2 |
| #11718590 | 2 |
| C13×#336 | 2 |
| #2015 | 13 |