Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2142 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2142 conjugacy classes of subgroups — too many to draw. Only its 747 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 |
|---|---|---|
| 3. C2×#5069 | C2 | direct (N × H) |
| 17. #5069 | C22 | direct (N × H) |
| 140. C22×C3 | #491 | semidirect |
| 165. C2×C3 | C2×#491 | semidirect |
| 168. C22 | #5069 | direct (N × H) |
| 177. C3 | C22×#491 | semidirect |
| 178. C2 | C2×#5069 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#125 | 2 |
| C22×#869 | 2 |
| C2×#5069 | 2 |
| C22×#810 | 2 |
| C22×#803 | 2 |
| C22×#491 | 3 |