Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 360 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. #11719400 | C2 | semidirect |
| 2. C13×#499 | C2 | semidirect |
| 3. #11718727 | C2 | semidirect |
| 4. #11718546 | C2 | semidirect |
| 5. #11718543 | C2 | semidirect |
| 6. #11718526 | C2 | semidirect |
| 7. #11718522 | C2 | semidirect |
| 8. C4×D104 | C2 | semidirect |
| 9. #11718349 | C2 | semidirect |
| 84. #499 | D13 | semidirect |
| 163. C13 | #3355 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719400 | 2 |
| C13×#499 | 2 |
| #11718727 | 2 |
| #11718546 | 2 |
| #11718543 | 2 |
| #11718526 | 2 |
| #11718522 | 2 |
| C4×D104 | 2 |
| #11718349 | 2 |
| #3355 | 13 |