Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
992 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 218 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. C2×#88121 | C2 | direct (N × H) |
| 12. C2×#6122 | C22 | semidirect |
| 14. #88121 | C22 | direct (N × H) |
| 35. #6122 | C23 | semidirect |
| 72. C22×C13 | #100 | semidirect |
| 96. C2×C13 | C2×#100 | semidirect |
| 121. C13 | C22×#100 | semidirect |
| 157. C22 | #88121 | direct (N × H) |
| 167. C2 | C2×#88121 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊D13 | 2 |
| C22×#6122 | 2 |
| C2×#88121 | 2 |
| C22×#100 | 13 |