Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
204 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 3. #11718785 | C2 | semidirect |
| 5. C13×#344 | C2 | semidirect |
| 6. #11718151 | C2 | semidirect |
| 7. #11718123 | C2 | semidirect |
| 72. #344 | D13 | semidirect |
| 130. C13 | #2081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11718792 | 2 |
| C2×#88063 | 2 |
| #11718785 | 2 |
| #11718662 | 2 |
| C13×#344 | 2 |
| #11718151 | 2 |
| #11718123 | 2 |
| #2081 | 13 |