Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
356 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 38. #818 | Q8 | semidirect |
| 42. #812 | Q8 | semidirect |
| 184. C3 | #13457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#498 | 2 |
| C2×#4487 | 2 |
| #69794 | 2 |
| #67721 | 2 |
| #67658 | 2 |
| #13457 | 3 |