Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
756 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 249 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×#568 | C2 | semidirect |
| 3. #11719524 | C2 | semidirect |
| 4. #11718793 | C2 | semidirect |
| 5. C2×#88063 | C2 | semidirect |
| 14. C2×C13×M16 | C22 | semidirect |
| 16. C2×#6099 | C22 | semidirect |
| 17. #88064 | C22 | semidirect |
| 18. #88063 | C22 | semidirect |
| 65. #568 | D13 | semidirect |
| 88. C2×M16 | C2×D13 | semidirect |
| 118. C13 | #2888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88256 | 2 |
| C13×#568 | 2 |
| #11719524 | 2 |
| #11718793 | 2 |
| C2×#88063 | 2 |
| #2888 | 13 |