Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
836 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 169 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. C2×C13×C22⋊Q8 | C2 | semidirect |
| 3. C2×#88201 | C2 | semidirect |
| 4. C2×#88198 | C2 | semidirect |
| 5. C4×C22⋊Dic13 | C2 | semidirect |
| 6. #11718650 | C2 | semidirect |
| 7. #11718649 | C2 | semidirect |
| 8. #11718635 | C2 | semidirect |
| 9. #11718620 | C2 | semidirect |
| 104. C2×Dic13 | #41 | semidirect |
| 111. C2×C22⋊Q8 | D13 | semidirect |
| 206. C13 | #2432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6127 | 2 |
| C2×C13×C22⋊Q8 | 2 |
| C2×#88201 | 2 |
| C2×#88198 | 2 |
| C4×C22⋊Dic13 | 2 |
| #11718650 | 2 |
| #11718649 | 2 |
| #11718635 | 2 |
| #11718620 | 2 |
| #2432 | 13 |