Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 1. C13×#536 | C2 | semidirect |
| 3. C2×#88196 | C2 | semidirect |
| 4. #11719228 | C2 | semidirect |
| 5. #11718893 | C2 | semidirect |
| 6. C2×#88075 | C2 | semidirect |
| 7. #11718751 | C2 | semidirect |
| 8. #11718744 | C2 | semidirect |
| 9. #11718718 | C2 | semidirect |
| 10. #11718715 | C2 | semidirect |
| 11. #11718660 | C2 | semidirect |
| 124. #536 | D13 | semidirect |
| 233. C13 | #3046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#536 | 2 |
| C2×#88204 | 2 |
| C2×#88196 | 2 |
| #11719228 | 2 |
| #11718893 | 2 |
| C2×#88075 | 2 |
| #11718751 | 2 |
| #11718744 | 2 |
| #11718718 | 2 |
| #11718715 | 2 |
| #11718660 | 2 |
| #3046 | 13 |