Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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 |
|---|---|---|
| 2. #11719224 | C2 | semidirect |
| 3. #11718894 | C2 | semidirect |
| 4. #11718893 | C2 | semidirect |
| 5. #11718876 | C2 | semidirect |
| 6. C2×#88072 | C2 | semidirect |
| 7. #11718732 | C2 | semidirect |
| 8. #11718731 | C2 | semidirect |
| 9. #11718717 | C2 | semidirect |
| 10. #11718716 | C2 | semidirect |
| 11. #11718658 | C2 | semidirect |
| 27. #88124 | C22 | semidirect |
| 28. #88123 | C22 | semidirect |
| 29. #88075 | C22 | semidirect |
| 30. #88075 | C22 | semidirect |
| 31. #88075 | C22 | semidirect |
| 36. #88072 | C22 | semidirect |
| 37. #88072 | C22 | semidirect |
| 38. #88072 | C22 | semidirect |
| 39. #88043 | C22 | semidirect |
| 40. C4×#1055 | C22 | semidirect |
| 212. C13 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#535 | 2 |
| #11719224 | 2 |
| #11718894 | 2 |
| #11718893 | 2 |
| #11718876 | 2 |
| C2×#88072 | 2 |
| #11718732 | 2 |
| #11718731 | 2 |
| #11718717 | 2 |
| #11718716 | 2 |
| #11718658 | 2 |
| #3136 | 13 |