Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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×#88180 | C2 | semidirect |
| 3. #11718876 | C2 | semidirect |
| 4. #11718868 | C2 | semidirect |
| 5. #11718696 | C2 | semidirect |
| 6. #11718695 | C2 | semidirect |
| 7. #11718694 | C2 | semidirect |
| 8. #11718625 | C2 | semidirect |
| 22. #88180 | C22 | semidirect |
| 23. C2×C4⋊Dic13 | C22 | semidirect |
| 24. C2×C4⋊Dic13 | C22 | semidirect |
| 27. #88072 | C22 | semidirect |
| 28. #88072 | C22 | semidirect |
| 29. C22⋊#1055 | C22 | semidirect |
| 30. C22⋊#1055 | C22 | semidirect |
| 31. #88048 | C22 | semidirect |
| 32. #88047 | C22 | semidirect |
| 190. C13 | #3094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#121 | 2 |
| C2×#88180 | 2 |
| #11718876 | 2 |
| #11718868 | 2 |
| #11718696 | 2 |
| #11718695 | 2 |
| #11718694 | 2 |
| #11718625 | 2 |
| #3094 | 13 |