Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
524 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 237 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. #11718642 | C2 | semidirect |
| 5. C4×C4⋊Dic13 | C2 | semidirect |
| 6. #11718593 | C2 | semidirect |
| 7. C42×Dic13 | C2 | semidirect |
| 9. C13×#117 | C4 | semidirect |
| 80. #117 | Dic13 | semidirect |
| 115. C13 | #2298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#117 | 2 |
| C4×C22⋊Dic13 | 2 |
| #11718642 | 2 |
| #11718612 | 2 |
| C4×C4⋊Dic13 | 2 |
| #11718593 | 2 |
| C42×Dic13 | 2 |
| #2298 | 13 |