Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
396 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 109 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. #11719396 | C2 | semidirect |
| 3. C13×#490 | C2 | semidirect |
| 4. #11718735 | C2 | semidirect |
| 5. #11718730 | C2 | semidirect |
| 6. #11718448 | C2 | semidirect |
| 7. #11718444 | C2 | semidirect |
| 8. #11718442 | C2 | semidirect |
| 9. #11718428 | C2 | semidirect |
| 10. #11718376 | C2 | semidirect |
| 11. #11718366 | C2 | semidirect |
| 120. #490 | D13 | semidirect |
| 224. C13 | #3219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719421 | 2 |
| #11719396 | 2 |
| C13×#490 | 2 |
| #11718735 | 2 |
| #11718730 | 2 |
| #11718448 | 2 |
| #11718444 | 2 |
| #11718442 | 2 |
| #11718428 | 2 |
| #11718376 | 2 |
| #11718366 | 2 |
| #3219 | 13 |