Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
928 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 381 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. #11718590 | C2 | direct (N × H) |
| 12. C22×Dic26 | C4 | semidirect |
| 25. C22×C4×C13 | Q8 | semidirect |
| 38. C2×Dic26 | C2×C4 | semidirect |
| 55. C2×C4×C13 | C2×Q8 | semidirect |
| 96. C2×C13 | #391 | semidirect |
| 116. C22×C4 | Dic26 | semidirect |
| 124. C13 | C2×#391 | semidirect |
| 143. C2×C4 | C2×Dic26 | semidirect |
| 161. C2 | #11718590 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic26 | 2 |
| C22×C42×C13 | 2 |
| C22×C4⋊Dic13 | 2 |
| C2×#88071 | 2 |
| #11718590 | 2 |
| C2×#391 | 13 |