Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 133 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. C13×#547 | C2 | semidirect |
| 2. C2×#88204 | C2 | semidirect |
| 3. #11719256 | C2 | semidirect |
| 4. #11718900 | C2 | semidirect |
| 5. #11718753 | C2 | semidirect |
| 6. #11718744 | C2 | semidirect |
| 7. #11718712 | C2 | semidirect |
| 8. #11718708 | C2 | semidirect |
| 9. #11718680 | C2 | semidirect |
| 10. C4×#6104 | C2 | semidirect |
| 11. D4×#1055 | C2 | semidirect |
| 72. #6104 | D4 | semidirect |
| 116. #547 | D13 | semidirect |
| 139. C4×C13 | #135 | semidirect |
| 220. C13 | #3283 | semidirect |
| 268. C4 | #88204 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#547 | 2 |
| C2×#88204 | 2 |
| #11719256 | 2 |
| #11718900 | 2 |
| #11718753 | 2 |
| #11718744 | 2 |
| #11718712 | 2 |
| #11718708 | 2 |
| #11718680 | 2 |
| C4×#6104 | 2 |
| D4×#1055 | 2 |
| #3283 | 13 |