Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
392 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 121 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×#529 | C2 | semidirect |
| 2. #11719182 | C2 | semidirect |
| 3. #11718727 | C2 | semidirect |
| 4. #11718718 | C2 | semidirect |
| 5. #11718710 | C2 | semidirect |
| 6. #11718700 | C2 | semidirect |
| 7. #11718688 | C2 | semidirect |
| 8. #11718681 | C2 | semidirect |
| 9. #11718676 | C2 | semidirect |
| 10. #11718668 | C2 | semidirect |
| 11. #11718585 | C2 | semidirect |
| 116. #529 | D13 | semidirect |
| 223. C13 | #3251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#529 | 2 |
| #11719182 | 2 |
| #11718727 | 2 |
| #11718718 | 2 |
| #11718710 | 2 |
| #11718700 | 2 |
| #11718688 | 2 |
| #11718681 | 2 |
| #11718676 | 2 |
| #11718668 | 2 |
| #11718585 | 2 |
| #3251 | 13 |