Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11719396 | C2 | semidirect |
| 2. C13×#499 | C2 | semidirect |
| 3. #11718729 | C2 | semidirect |
| 4. #11718550 | C2 | semidirect |
| 5. #11718547 | C2 | semidirect |
| 6. #11718530 | C2 | semidirect |
| 7. #11718529 | C2 | semidirect |
| 9. #11718514 | C2 | semidirect |
| 10. #11718357 | C2 | semidirect |
| 11. C4×#6094 | C2 | semidirect |
| 93. #499 | D13 | semidirect |
| 178. C13 | #3183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719396 | 2 |
| C13×#499 | 2 |
| #11718729 | 2 |
| #11718550 | 2 |
| #11718547 | 2 |
| #11718530 | 2 |
| #11718529 | 2 |
| #11718526 | 2 |
| #11718514 | 2 |
| #11718357 | 2 |
| C4×#6094 | 2 |
| #3183 | 13 |