Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
314 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 144 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. #11719158 | C2 | semidirect |
| 5. #11719080 | C2 | semidirect |
| 6. #11719078 | C2 | semidirect |
| 7. #11719078 | C2 | semidirect |
| 167. C13 | #2987 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719327 | 2 |
| #11719158 | 2 |
| #11719130 | 2 |
| #11719128 | 2 |
| #11719080 | 2 |
| #11719078 | 2 |
| #11719068 | 2 |
| #2987 | 13 |