Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 197 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. C2×#88141 | C2 | semidirect |
| 5. #11718637 | C2 | semidirect |
| 6. #11718607 | C2 | semidirect |
| 7. #11718606 | C2 | semidirect |
| 8. #11718593 | C2 | semidirect |
| 9. #11718590 | C2 | semidirect |
| 18. #88190 | C4 | semidirect |
| 46. C2×Dic26 | C2×C4 | semidirect |
| 51. C22⋊Dic13 | C2×C4 | semidirect |
| 56. C4×Dic13 | C2×C4 | semidirect |
| 169. C13 | #2326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88190 | 2 |
| C2×D4×Dic13 | 2 |
| C2×#88141 | 2 |
| C13×#390 | 2 |
| #11718637 | 2 |
| #11718607 | 2 |
| #11718606 | 2 |
| #11718593 | 2 |
| #11718590 | 2 |
| #2326 | 13 |