Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 125 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×#532 | C2 | semidirect |
| 2. #11719184 | C2 | semidirect |
| 3. #11718750 | C2 | semidirect |
| 4. #11718741 | C2 | semidirect |
| 5. #11718735 | C2 | semidirect |
| 6. #11718732 | C2 | semidirect |
| 7. #11718703 | C2 | semidirect |
| 8. #11718700 | C2 | semidirect |
| 9. C4×#6105 | C2 | semidirect |
| 10. C4×#6104 | C2 | semidirect |
| 11. C4×#6099 | C2 | semidirect |
| 111. #1055 | #41 | semidirect |
| 112. #532 | D13 | semidirect |
| 219. C13 | #3171 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#532 | 2 |
| #11719184 | 2 |
| #11718750 | 2 |
| #11718741 | 2 |
| #11718735 | 2 |
| #11718732 | 2 |
| #11718703 | 2 |
| #11718700 | 2 |
| C4×#6105 | 2 |
| C4×#6104 | 2 |
| C4×#6099 | 2 |
| #3171 | 13 |