Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
588 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 277 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 |
|---|---|---|
| 19. #88123 | C4 | direct (N × H) |
| 36. C42×C13 | Q8 | semidirect |
| 78. C4×C13 | C4×Q8 | semidirect |
| 79. C4×C13 | C4⋊Q8 | semidirect |
| 118. C42 | Dic26 | semidirect |
| 121. C13 | C4×C4⋊Q8 | semidirect |
| 151. C4 | C4×Dic26 | semidirect |
| 152. C4 | #88123 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88123 | 2 |
| C2×C4×Dic26 | 2 |
| C43×C13 | 2 |
| #11718596 | 2 |
| C4×C4⋊Dic13 | 2 |
| #11718590 | 2 |
| #11718589 | 2 |
| C4×C4⋊Q8 | 13 |