Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
504 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 233 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 |
|---|---|---|
| 4. #11718646 | C2 | semidirect |
| 5. C4⋊C4×Dic13 | C2 | semidirect |
| 7. #11718598 | C2 | semidirect |
| 8. C4×C4⋊Dic13 | C2 | semidirect |
| 10. C13×#117 | C4 | semidirect |
| 98. #117 | Dic13 | semidirect |
| 140. C13 | #2347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#117 | 2 |
| #11718873 | 2 |
| C4×C22⋊Dic13 | 2 |
| #11718646 | 2 |
| C4⋊C4×Dic13 | 2 |
| #11718612 | 2 |
| #11718598 | 2 |
| C4×C4⋊Dic13 | 2 |
| #2347 | 13 |