Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
390 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 2. C2×C3×#362 | C2 | semidirect |
| 3. #72061 | C2 | semidirect |
| 6. #70685 | C2 | semidirect |
| 7. #67818 | C2 | semidirect |
| 28. C2×#362 | D3 | semidirect |
| 313. C3 | #13397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83887 | 2 |
| C2×C3×#362 | 2 |
| #72061 | 2 |
| #71438 | 2 |
| #70719 | 2 |
| #70685 | 2 |
| #67818 | 2 |
| #13397 | 3 |