Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
362 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 148 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 |
| 3. #11719128 | C2 | semidirect |
| 4. C4×#6122 | C2 | semidirect |
| 5. #11719077 | C2 | semidirect |
| 6. #11719075 | C2 | semidirect |
| 7. #11719072 | C2 | semidirect |
| 8. #11719066 | C2 | semidirect |
| 9. #11719065 | C2 | semidirect |
| 178. C13 | #2967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719329 | 2 |
| #11719158 | 2 |
| #11719128 | 2 |
| C4×#6122 | 2 |
| #11719077 | 2 |
| #11719075 | 2 |
| #11719072 | 2 |
| #11719066 | 2 |
| #11719065 | 2 |
| #2967 | 13 |