Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
300 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 90 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. C2×C8×#261 | C2 | semidirect |
| 4. #11719072 | C2 | semidirect |
| 6. #11718268 | C2 | semidirect |
| 7. #11718247 | C2 | semidirect |
| 10. #88240 | C4 | semidirect |
| 19. #88118 | C4 | semidirect |
| 23. C13×#103 | C4 | semidirect |
| 24. #88075 | C4 | semidirect |
| 25. #88061 | C4 | semidirect |
| 26. #88049 | C4 | semidirect |
| 124. #103 | #261 | semidirect |
| 168. C13 | #1764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88240 | 2 |
| C2×#88118 | 2 |
| C2×C8×#261 | 2 |
| #11719072 | 2 |
| #11718465 | 2 |
| #11718268 | 2 |
| #11718247 | 2 |
| #1764 | 13 |