Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
392 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 113 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. #11719421 | C2 | semidirect |
| 2. #11719285 | C2 | semidirect |
| 3. C13×#460 | C2 | semidirect |
| 4. #11718835 | C2 | semidirect |
| 5. #11718826 | C2 | semidirect |
| 6. #11718733 | C2 | semidirect |
| 7. #11718681 | C2 | semidirect |
| 8. #11718507 | C2 | semidirect |
| 9. #11718498 | C2 | semidirect |
| 10. #11718443 | C2 | semidirect |
| 11. #11718427 | C2 | semidirect |
| 123. #460 | 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 |
|---|---|
| #11719421 | 2 |
| #11719285 | 2 |
| C13×#460 | 2 |
| #11718835 | 2 |
| #11718826 | 2 |
| #11718733 | 2 |
| #11718681 | 2 |
| #11718507 | 2 |
| #11718498 | 2 |
| #11718443 | 2 |
| #11718427 | 2 |
| #3251 | 13 |