Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
126 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 47 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. #11718341 | C2 | semidirect |
| 3. C13×#364 | C2 | semidirect |
| 5. #11718105 | C2 | semidirect |
| 23. Dic52 | Q8 | semidirect |
| 24. D104 | Q8 | semidirect |
| 46. #364 | D13 | semidirect |
| 81. C13 | #2230 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11718361 | 2 |
| #11718341 | 2 |
| C13×#364 | 2 |
| #11718110 | 2 |
| #11718105 | 2 |
| #2230 | 13 |