Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
754 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 169 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. C2×#88205 | C2 | semidirect |
| 3. C2×#88178 | C2 | semidirect |
| 4. #11718900 | C2 | semidirect |
| 5. #11718893 | C2 | semidirect |
| 6. #11718889 | C2 | semidirect |
| 7. #11718879 | C2 | semidirect |
| 8. #11718868 | C2 | semidirect |
| 19. C22×Dic26 | C22 | semidirect |
| 22. C2×#6107 | C22 | semidirect |
| 23. C2×#6105 | C22 | semidirect |
| 24. C2×C4⋊Dic13 | C22 | semidirect |
| 28. #88178 | C22 | semidirect |
| 30. C2×#6099 | C22 | semidirect |
| 31. #88075 | C22 | semidirect |
| 32. #88072 | C22 | semidirect |
| 34. C22⋊#1055 | C22 | semidirect |
| 139. C22×C13 | #137 | semidirect |
| 224. C13 | #3007 | semidirect |
| 276. C22 | #88205 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×#41 | 2 |
| C2×#88205 | 2 |
| C2×#88178 | 2 |
| #11718900 | 2 |
| #11718893 | 2 |
| #11718889 | 2 |
| #11718879 | 2 |
| #11718868 | 2 |
| #3007 | 13 |