Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
444 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11719484 | C2 | semidirect |
| 2. #11719471 | C2 | semidirect |
| 3. #11719458 | C2 | semidirect |
| 4. C13×#473 | C2 | semidirect |
| 5. #11718866 | C2 | semidirect |
| 6. #11718842 | C2 | semidirect |
| 7. #11718805 | C2 | semidirect |
| 8. #11718557 | C2 | semidirect |
| 9. #11718556 | C2 | semidirect |
| 10. #11718416 | C2 | semidirect |
| 11. #11718413 | C2 | semidirect |
| 136. #473 | D13 | semidirect |
| 240. C13 | #3293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719484 | 2 |
| #11719471 | 2 |
| #11719458 | 2 |
| C13×#473 | 2 |
| #11718866 | 2 |
| #11718842 | 2 |
| #11718805 | 2 |
| #11718557 | 2 |
| #11718556 | 2 |
| #11718416 | 2 |
| #11718413 | 2 |
| #3293 | 13 |