Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
446 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 119 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. #11718813 | C2 | semidirect |
| 4. #11718812 | C2 | semidirect |
| 5. #11718796 | C2 | semidirect |
| 6. M16×Dic13 | C2 | semidirect |
| 7. #11718700 | C2 | semidirect |
| 8. #11718530 | C2 | semidirect |
| 9. #11718516 | C2 | semidirect |
| 10. #11718446 | C2 | semidirect |
| 11. #11718421 | C2 | semidirect |
| 95. C8×C13 | #41 | semidirect |
| 97. #1055 | #41 | semidirect |
| 104. #469 | D13 | semidirect |
| 188. C13 | #3184 | semidirect |
| 215. C8 | #6129 | 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 |
| #11718813 | 2 |
| #11718812 | 2 |
| #11718796 | 2 |
| M16×Dic13 | 2 |
| #11718700 | 2 |
| #11718530 | 2 |
| #11718516 | 2 |
| #11718446 | 2 |
| #11718421 | 2 |
| #3184 | 13 |