Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
312 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 105 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. #11718586 | C2 | semidirect |
| 3. #11718585 | C2 | semidirect |
| 4. D4⋊#1055 | C2 | semidirect |
| 18. C4⋊#1055 | C22 | semidirect |
| 19. C4×#1055 | C22 | semidirect |
| 51. D4×C13 | M16 | semidirect |
| 132. C13 | #1486 | semidirect |
| 140. D4 | #6099 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D4×C13 | 2 |
| #11718586 | 2 |
| #11718585 | 2 |
| D4⋊#1055 | 2 |
| #1486 | 13 |