Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
562 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 1. C2×C3×#500 | C2 | semidirect |
| 3. C2×#4546 | C2 | semidirect |
| 5. #67654 | C2 | semidirect |
| 20. C2×#500 | D3 | semidirect |
| 256. C3 | #10278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#500 | 2 |
| C2×#5084 | 2 |
| C2×#4546 | 2 |
| #69787 | 2 |
| #67654 | 2 |
| #10278 | 3 |