Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
336 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 28. Dic52 | Q8 | direct (N × H) |
| 30. Q8×C13 | Q16 | semidirect |
| 79. C13 | Q8×Q16 | semidirect |
| 83. Q8 | Dic52 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic26 | 2 |
| C8×Q8×C13 | 2 |
| #11718511 | 2 |
| C4×Dic52 | 2 |
| #11718343 | 2 |
| Q8×Q16 | 13 |