Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
152 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 49 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. C3×#1367 | C2 | semidirect |
| 3. #67439 | C2 | semidirect |
| 14. #1367 | D3 | semidirect |
| 136. C3 | #7092 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #68060 | 2 |
| C3×#1367 | 2 |
| #67439 | 2 |
| #7092 | 3 |