Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
444 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 444 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 |
| 4. #11718680 | C2 | semidirect |
| 5. #11718679 | C2 | semidirect |
| 6. #11718668 | C2 | semidirect |
| 7. #11718631 | C2 | semidirect |
| 8. #11718587 | C2 | semidirect |
| 23. #88123 | C22 | semidirect |
| 24. #88123 | C22 | semidirect |
| 26. C4×Dic26 | C22 | semidirect |
| 29. #88050 | C22 | semidirect |
| 30. #88047 | C22 | semidirect |
| 31. C4⋊#1055 | C22 | semidirect |
| 32. #88043 | C22 | semidirect |
| 176. C13 | #3110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D4×C13 | 2 |
| #11719175 | 2 |
| #11718879 | 2 |
| #11718680 | 2 |
| #11718679 | 2 |
| #11718668 | 2 |
| #11718631 | 2 |
| #11718587 | 2 |
| #3110 | 13 |