Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
368 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×C13×C22⋊C8 | C2 | semidirect |
| 3. #11718873 | C2 | semidirect |
| 4. C2×#88061 | C2 | semidirect |
| 5. C2×#88061 | C2 | semidirect |
| 6. C2×#88058 | C2 | semidirect |
| 7. #11718143 | C2 | semidirect |
| 52. C2×C8×C13 | D4 | semidirect |
| 110. C2×C22⋊C8 | D13 | semidirect |
| 195. C2×C8 | C22⋊D13 | semidirect |
| 204. C13 | #2033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88184 | 2 |
| C2×C13×C22⋊C8 | 2 |
| #11718873 | 2 |
| C2×#88061 | 2 |
| C2×#88058 | 2 |
| #11718143 | 2 |
| #2033 | 13 |