Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
398 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 123 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×#555 | C2 | semidirect |
| 2. #11719256 | C2 | semidirect |
| 3. #11718754 | C2 | semidirect |
| 4. #11718745 | C2 | semidirect |
| 5. #11718702 | C2 | semidirect |
| 6. #11718698 | C2 | semidirect |
| 7. #11718680 | C2 | semidirect |
| 8. C4×#6104 | C2 | semidirect |
| 9. D4×#1055 | C2 | semidirect |
| 10. #11718663 | C2 | semidirect |
| 11. #11718657 | C2 | semidirect |
| 106. #555 | D13 | semidirect |
| 206. C13 | #3303 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#555 | 2 |
| #11719256 | 2 |
| #11718754 | 2 |
| #11718745 | 2 |
| #11718702 | 2 |
| #11718698 | 2 |
| #11718680 | 2 |
| C4×#6104 | 2 |
| D4×#1055 | 2 |
| #11718663 | 2 |
| #11718657 | 2 |
| #3303 | 13 |