Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
158 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 27. C3⋊C32 | Q8 | semidirect |
| 105. C3 | #13731 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2252 | 2 |
| #69044 | 2 |
| #67575 | 2 |
| C4×C3⋊C32 | 2 |
| #13731 | 3 |