Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
430 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 430 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. #11719301 | C2 | semidirect |
| 2. C13×#469 | C2 | semidirect |
| 3. #11718811 | C2 | semidirect |
| 4. #11718796 | C2 | semidirect |
| 5. #11718779 | C2 | semidirect |
| 6. #11718700 | C2 | semidirect |
| 7. #11718531 | C2 | semidirect |
| 8. #11718447 | C2 | semidirect |
| 9. #11718422 | C2 | semidirect |
| 97. #469 | D13 | semidirect |
| 177. C13 | #3253 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719301 | 2 |
| C13×#469 | 2 |
| #11718811 | 2 |
| #11718796 | 2 |
| #11718779 | 2 |
| #11718700 | 2 |
| #11718531 | 2 |
| #11718447 | 2 |
| #11718422 | 2 |
| #3253 | 13 |