Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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×#88178 | C2 | semidirect |
| 3. #11718879 | C2 | semidirect |
| 4. #11718868 | C2 | semidirect |
| 5. #11718703 | C2 | semidirect |
| 6. #11718701 | C2 | semidirect |
| 7. #11718694 | C2 | semidirect |
| 8. #11718631 | C2 | semidirect |
| 12. C22×Dic26 | C22 | semidirect |
| 20. C2×#6105 | C22 | semidirect |
| 21. C2×C4⋊Dic13 | C22 | semidirect |
| 25. #88178 | C22 | semidirect |
| 27. C2×#6099 | C22 | semidirect |
| 28. #88072 | C22 | semidirect |
| 30. C22⋊#1055 | C22 | semidirect |
| 31. #88050 | C22 | semidirect |
| 32. #88047 | C22 | semidirect |
| 196. C13 | #3193 | 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×#88178 | 2 |
| #11718879 | 2 |
| #11718868 | 2 |
| #11718703 | 2 |
| #11718701 | 2 |
| #11718694 | 2 |
| #11718631 | 2 |
| #3193 | 13 |