Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 15. #88043 | C4 | semidirect |
| 16. C4×#1055 | C4 | semidirect |
| 112. C13 | #1841 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6099 | 2 |
| C13×#339 | 2 |
| #11718152 | 2 |
| #11718151 | 2 |
| #11718125 | 2 |
| #11718123 | 2 |
| #11718115 | 2 |
| #1841 | 13 |