Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
384 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 4. C2×C4×#1055 | C2 | semidirect |
| 5. #11718116 | C2 | semidirect |
| 10. C22×#1055 | C4 | semidirect |
| 15. C22⋊#1055 | C4 | semidirect |
| 25. C13×C22⋊C4 | C8 | semidirect |
| 49. C2×C4×C13 | C2×C8 | semidirect |
| 56. #1055 | C22⋊C4 | direct (N × H) |
| 65. C22×C13 | C4×C8 | semidirect |
| 107. C22⋊C4 | #1055 | direct (N × H) |
| 110. C13 | C8×C22⋊C4 | semidirect |
| 122. C2×C4 | C2×#1055 | semidirect |
| 134. C22 | C4×#1055 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1055 | 2 |
| C4×C13×C22⋊C4 | 2 |
| C2×C22⋊#1055 | 2 |
| C2×C4×#1055 | 2 |
| #11718116 | 2 |
| C8×C22⋊C4 | 13 |