Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
378 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11718798 | C2 | semidirect |
| 4. #11718777 | C2 | semidirect |
| 5. #11718400 | C2 | semidirect |
| 6. #11718384 | C2 | semidirect |
| 135. C13 | #3202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719530 | 2 |
| C13×#408 | 2 |
| #11718798 | 2 |
| #11718777 | 2 |
| #11718400 | 2 |
| #11718384 | 2 |
| #3202 | 13 |