Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
416 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 181 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. #11718682 | C2 | direct (N × H) |
| 25. C2×Q8×C13 | Q8 | semidirect |
| 50. Q8×C13 | C2×Q8 | semidirect |
| 101. C2×C13 | #477 | semidirect |
| 109. C2×Q8 | Dic26 | semidirect |
| 128. C13 | C2×#477 | semidirect |
| 133. Q8 | C2×Dic26 | semidirect |
| 161. C2 | #11718682 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Q8×C13 | 2 |
| C2×#88123 | 2 |
| C2×#88075 | 2 |
| #11718682 | 2 |
| C2×#88047 | 2 |
| C2×C4⋊#1055 | 2 |
| C2×#477 | 13 |