Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 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×#520 | C2 | semidirect |
| 3. #11718895 | C2 | semidirect |
| 4. #11718664 | C2 | semidirect |
| 5. #11718664 | C2 | semidirect |
| 6. #11718662 | C2 | semidirect |
| 7. #11718659 | C2 | semidirect |
| 8. #11718629 | C2 | semidirect |
| 9. #11718628 | C2 | semidirect |
| 10. C2×#88049 | C2 | semidirect |
| 11. #11718625 | C2 | semidirect |
| 18. C13×#117 | C22 | semidirect |
| 20. C2×C13×C4⋊C4 | C22 | semidirect |
| 29. C22⋊#1055 | C22 | semidirect |
| 30. C22⋊#1055 | C22 | semidirect |
| 35. #88048 | C22 | semidirect |
| 36. #88048 | C22 | semidirect |
| 37. #88048 | C22 | semidirect |
| 38. #88047 | C22 | semidirect |
| 39. #88047 | C22 | semidirect |
| 40. #88047 | C22 | semidirect |
| 110. #520 | D13 | semidirect |
| 154. #117 | C2×D13 | semidirect |
| 156. C2×C4⋊C4 | C2×D13 | semidirect |
| 211. C13 | #3096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#520 | 2 |
| #11719535 | 2 |
| #11718895 | 2 |
| #11718664 | 2 |
| #11718662 | 2 |
| #11718659 | 2 |
| #11718629 | 2 |
| #11718628 | 2 |
| C2×#88049 | 2 |
| #11718625 | 2 |
| #3096 | 13 |