Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1504 conjugacy classes of subgroups; only the 770 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 770 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. C22×#6122 | C2 | semidirect |
| 3. C23×#1057 | C2 | semidirect |
| 4. C2×#88238 | C2 | direct (N × H) |
| 5. C22×#6118 | C2 | semidirect |
| 6. C22×D13⋊C8 | C2 | semidirect |
| 14. C2×#6122 | C22 | semidirect |
| 18. C22×#1057 | C22 | semidirect |
| 19. #88238 | C22 | direct (N × H) |
| 20. C2×#6118 | C22 | semidirect |
| 21. C2×D13⋊C8 | C22 | semidirect |
| 36. #6122 | C23 | semidirect |
| 40. C2×#1057 | C23 | semidirect |
| 41. #6118 | C23 | semidirect |
| 42. D13⋊C8 | C23 | semidirect |
| 70. C22×C13 | #131 | semidirect |
| 95. C2×C13 | C2×#131 | semidirect |
| 119. C13 | C22×#131 | semidirect |
| 142. C22 | #88238 | direct (N × H) |
| 151. C2 | C2×#88238 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6129 | 2 |
| C22×#6122 | 2 |
| C23×#1057 | 2 |
| C2×#88238 | 2 |
| C22×#6118 | 2 |
| C22×D13⋊C8 | 2 |
| C22×#131 | 13 |