Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
274 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 67 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. #11718898 | C2 | semidirect |
| 3. #11718897 | C2 | semidirect |
| 4. C2×#88073 | C2 | semidirect |
| 5. #11718876 | C2 | semidirect |
| 6. #11718785 | C2 | semidirect |
| 7. #11718151 | C2 | semidirect |
| 168. C13 | #2048 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×AGL(1,ℤ/8) | 2 |
| #11718898 | 2 |
| #11718897 | 2 |
| C2×#88073 | 2 |
| #11718876 | 2 |
| #11718785 | 2 |
| #11718151 | 2 |
| #2048 | 13 |