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. #11719430 | C2 | semidirect |
| 2. #11719285 | C2 | semidirect |
| 3. C13×#475 | C2 | semidirect |
| 4. #11718748 | C2 | semidirect |
| 5. #11718688 | C2 | semidirect |
| 6. #11718532 | C2 | semidirect |
| 7. #11718526 | C2 | semidirect |
| 8. #11718504 | C2 | semidirect |
| 9. #11718498 | C2 | semidirect |
| 10. #11718480 | C2 | semidirect |
| 11. #11718473 | C2 | semidirect |
| 118. #475 | 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 |
|---|---|
| #11719430 | 2 |
| #11719285 | 2 |
| C13×#475 | 2 |
| #11718748 | 2 |
| #11718688 | 2 |
| #11718532 | 2 |
| #11718526 | 2 |
| #11718504 | 2 |
| #11718498 | 2 |
| #11718480 | 2 |
| #11718473 | 2 |
| #3251 | 13 |