Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
318 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 83 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×#88056 | C2 | semidirect |
| 5. C2×#88056 | C2 | semidirect |
| 6. #11718589 | C2 | semidirect |
| 7. C13×#336 | C2 | semidirect |
| 105. #336 | D13 | semidirect |
| 188. C13 | #2042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88129 | 2 |
| C2×#88061 | 2 |
| C2×#88056 | 2 |
| #11718589 | 2 |
| C13×#336 | 2 |
| #2042 | 13 |