Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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×#550 | C2 | semidirect |
| 2. C2×#88204 | C2 | semidirect |
| 3. #11719258 | C2 | semidirect |
| 4. #11718899 | C2 | semidirect |
| 5. #11718736 | C2 | semidirect |
| 6. #11718734 | C2 | semidirect |
| 7. #11718699 | C2 | semidirect |
| 8. #11718698 | C2 | semidirect |
| 9. C4×#6107 | C2 | semidirect |
| 10. #11718688 | C2 | semidirect |
| 11. D4×#1055 | C2 | semidirect |
| 69. #6107 | D4 | semidirect |
| 120. #550 | D13 | semidirect |
| 143. C4×C13 | #135 | semidirect |
| 224. C13 | #3287 | semidirect |
| 276. C4 | #88204 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#550 | 2 |
| C2×#88204 | 2 |
| #11719258 | 2 |
| #11718899 | 2 |
| #11718736 | 2 |
| #11718734 | 2 |
| #11718699 | 2 |
| #11718698 | 2 |
| C4×#6107 | 2 |
| #11718688 | 2 |
| D4×#1055 | 2 |
| #3287 | 13 |