Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. #11719175 | C2 | semidirect |
| 3. #11718886 | C2 | semidirect |
| 5. #11718717 | C2 | semidirect |
| 6. #11718716 | C2 | semidirect |
| 7. C4×#6099 | C2 | semidirect |
| 18. #88124 | C22 | semidirect |
| 19. #88123 | C22 | semidirect |
| 21. #88075 | C22 | semidirect |
| 23. #88043 | C22 | semidirect |
| 24. C4×#1055 | C22 | semidirect |
| 131. C13 | #3140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#124 | 2 |
| #11719175 | 2 |
| #11718886 | 2 |
| #11718876 | 2 |
| #11718717 | 2 |
| #11718716 | 2 |
| C4×#6099 | 2 |
| #3140 | 13 |