Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
312 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #11718665 | C2 | semidirect |
| 5. #11718123 | C2 | semidirect |
| 10. #88198 | C4 | semidirect |
| 11. #88190 | C4 | semidirect |
| 124. C13 | #1909 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719530 | 2 |
| #11719524 | 2 |
| C13×#410 | 2 |
| #11718665 | 2 |
| #11718123 | 2 |
| #1909 | 13 |