Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
492 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 3. C22×Dic52 | C2 | semidirect |
| 4. #11718798 | C2 | direct (N × H) |
| 5. C2×#88057 | C2 | semidirect |
| 6. C2×#88056 | C2 | semidirect |
| 19. C2×Dic52 | C22 | semidirect |
| 20. #88057 | C22 | semidirect |
| 21. #88056 | C22 | semidirect |
| 102. C2×C13 | #470 | semidirect |
| 128. C13 | C2×#470 | semidirect |
| 164. C2 | #11718798 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×M16 | 2 |
| C2×#88178 | 2 |
| C22×Dic52 | 2 |
| #11718798 | 2 |
| C2×#88057 | 2 |
| C2×#88056 | 2 |
| C2×#470 | 13 |