Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
374 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 123 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. #11719247 | C2 | semidirect |
| 3. #11718755 | C2 | semidirect |
| 4. #11718739 | C2 | semidirect |
| 5. #11718703 | C2 | semidirect |
| 6. #11718696 | C2 | semidirect |
| 7. C4×#6105 | C2 | semidirect |
| 8. #11718673 | C2 | semidirect |
| 9. #11718668 | C2 | semidirect |
| 10. #11718631 | C2 | semidirect |
| 11. #11718625 | C2 | semidirect |
| 100. #1055 | #41 | semidirect |
| 196. C13 | #3353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#547 | 2 |
| #11719247 | 2 |
| #11718755 | 2 |
| #11718739 | 2 |
| #11718703 | 2 |
| #11718696 | 2 |
| C4×#6105 | 2 |
| #11718673 | 2 |
| #11718668 | 2 |
| #11718631 | 2 |
| #11718625 | 2 |
| #3353 | 13 |