Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
312 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 14. C2×#6107 | C4 | semidirect |
| 68. C2×C4×C13 | Q16 | semidirect |
| 159. C13 | #1969 | semidirect |
| 181. C2×C4 | #6107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6107 | 2 |
| C13×#391 | 2 |
| C2×#88075 | 2 |
| C2×#88050 | 2 |
| C2×#88047 | 2 |
| #11718590 | 2 |
| C2×C4×#1055 | 2 |
| #1969 | 13 |