Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
480 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 5. #11718751 | C2 | direct (N × H) |
| 57. C2×C4×C13 | Q16 | semidirect |
| 85. C4×C13 | C2×Q16 | semidirect |
| 107. C2×C13 | #462 | semidirect |
| 136. C13 | C2×#462 | semidirect |
| 151. C2×C4 | #6107 | semidirect |
| 168. C4 | C2×#6107 | semidirect |
| 171. C2 | #11718751 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×C4⋊Q8 | 2 |
| C22×#6107 | 2 |
| C2×C4×Dic26 | 2 |
| C2×#88075 | 2 |
| #11718751 | 2 |
| C2×C4⋊#1055 | 2 |
| C2×#462 | 13 |