Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1460 conjugacy classes of subgroups; only the 754 normal subgroups are shown.
This group has 1460 conjugacy classes of subgroups — too many to draw. Only its 754 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. #11719625 | C2 | direct (N × H) |
| 3. C2×#88240 | C2 | semidirect |
| 4. C2×D13⋊M16 | C2 | semidirect |
| 13. #88240 | C22 | semidirect |
| 14. D13⋊M16 | C22 | semidirect |
| 15. C2×#6118 | C22 | semidirect |
| 16. C2×D13⋊C8 | C22 | semidirect |
| 33. #6118 | C23 | semidirect |
| 34. D13⋊C8 | C23 | semidirect |
| 79. C2×C13 | #568 | semidirect |
| 100. C13 | C2×#568 | semidirect |
| 129. C2 | #11719625 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6131 | 2 |
| #11719625 | 2 |
| C2×#88240 | 2 |
| C2×D13⋊M16 | 2 |
| C2×#568 | 13 |