Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
180 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 84 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. #11718256 | C2 | semidirect |
| 5. #11718255 | C2 | semidirect |
| 31. #6099 | C8 | semidirect |
| 50. #1055 | C2×C8 | semidirect |
| 99. C13 | #1565 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719119 | 2 |
| C2×C4⋊#1057 | 2 |
| M16×Dic13 | 2 |
| #11718256 | 2 |
| #11718255 | 2 |
| #1565 | 13 |