Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
340 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. #11718891 | C2 | semidirect |
| 3. C2×#88075 | C2 | semidirect |
| 6. C2×#88058 | C2 | semidirect |
| 7. C2×#88055 | C2 | semidirect |
| 12. C2×C13×SD16 | C4 | semidirect |
| 87. C8×C13 | C22⋊C4 | semidirect |
| 118. C2×SD16 | Dic13 | semidirect |
| 168. C13 | #1973 | semidirect |
| 200. C8 | C22⋊Dic13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×SD16 | 2 |
| #11718891 | 2 |
| C2×#88075 | 2 |
| #11718882 | 2 |
| C2×#88072 | 2 |
| C2×#88058 | 2 |
| C2×#88055 | 2 |
| #1973 | 13 |