Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×C13×#137 | C2 | semidirect |
| 2. #11719530 | C2 | semidirect |
| 4. #11719521 | C2 | semidirect |
| 5. C22×#6107 | C2 | semidirect |
| 6. C2×#88163 | C2 | semidirect |
| 7. #11718851 | C2 | semidirect |
| 8. #11718842 | C2 | semidirect |
| 9. #11718829 | C2 | semidirect |
| 10. #11718828 | C2 | semidirect |
| 11. #11718783 | C2 | semidirect |
| 125. C2×#137 | D13 | semidirect |
| 231. C13 | #3156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#137 | 2 |
| #11719530 | 2 |
| C2×#88204 | 2 |
| #11719521 | 2 |
| C22×#6107 | 2 |
| C2×#88163 | 2 |
| #11718851 | 2 |
| #11718842 | 2 |
| #11718829 | 2 |
| #11718828 | 2 |
| #11718783 | 2 |
| #3156 | 13 |