Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
752 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 165 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. #11719530 | C2 | semidirect |
| 3. C2×#88205 | C2 | semidirect |
| 4. C22×#6105 | C2 | semidirect |
| 5. #11718900 | C2 | semidirect |
| 6. #11718895 | C2 | semidirect |
| 7. #11718894 | C2 | semidirect |
| 8. #11718879 | C2 | semidirect |
| 9. #11718876 | C2 | semidirect |
| 20. C22×Dic26 | C22 | semidirect |
| 23. C2×#6107 | C22 | semidirect |
| 27. C2×#6105 | C22 | semidirect |
| 28. C2×#6105 | C22 | semidirect |
| 29. #88180 | C22 | semidirect |
| 30. #88178 | C22 | semidirect |
| 31. C2×#6099 | C22 | semidirect |
| 32. C22×#1055 | C22 | semidirect |
| 33. #88075 | C22 | semidirect |
| 34. #88072 | C22 | semidirect |
| 35. #88072 | C22 | semidirect |
| 36. C22⋊#1055 | C22 | semidirect |
| 229. C13 | #3009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×H(5,𝔽2) | 2 |
| #11719530 | 2 |
| C2×#88205 | 2 |
| C22×#6105 | 2 |
| #11718900 | 2 |
| #11718895 | 2 |
| #11718894 | 2 |
| #11718879 | 2 |
| #11718876 | 2 |
| #3009 | 13 |