Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
756 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 202 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 | semidirect |
| 4. #11719148 | C2 | direct (N × H) |
| 5. C2×#88113 | C2 | semidirect |
| 21. C2×#6122 | C22 | semidirect |
| 23. #88121 | C22 | semidirect |
| 24. #88113 | C22 | semidirect |
| 161. C2×C13 | #413 | semidirect |
| 207. C13 | C2×#413 | semidirect |
| 277. C2 | #11719148 | 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 |
| C2×#88121 | 2 |
| #11719148 | 2 |
| C2×#88113 | 2 |
| C2×#413 | 13 |