Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
384 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 154 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 |
|---|---|---|
| 3. #11719130 | C2 | semidirect |
| 4. #11719128 | C2 | semidirect |
| 5. #11719079 | C2 | semidirect |
| 6. #11719068 | C2 | semidirect |
| 7. C4×#6118 | C2 | semidirect |
| 8. #11719047 | C2 | semidirect |
| 164. C13 | #2923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6129 | 2 |
| #11719147 | 2 |
| #11719130 | 2 |
| #11719128 | 2 |
| #11719079 | 2 |
| #11719068 | 2 |
| C4×#6118 | 2 |
| #11719047 | 2 |
| #2923 | 13 |