Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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. C13×#536 | C2 | semidirect |
| 3. C22×#6107 | C2 | semidirect |
| 4. C2×#88196 | C2 | semidirect |
| 5. #11718895 | C2 | semidirect |
| 6. #11718711 | C2 | semidirect |
| 7. #11718708 | C2 | semidirect |
| 8. #11718665 | C2 | semidirect |
| 9. #11718663 | C2 | semidirect |
| 124. #536 | D13 | semidirect |
| 223. C13 | #3011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88257 | 2 |
| C13×#536 | 2 |
| C22×#6107 | 2 |
| C2×#88196 | 2 |
| #11718895 | 2 |
| #11718711 | 2 |
| #11718708 | 2 |
| #11718665 | 2 |
| #11718663 | 2 |
| #3011 | 13 |