Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
972 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 972 conjugacy classes of subgroups — too many to draw. Only its 271 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×#5125 | C2 | semidirect |
| 3. C2×C3×#338 | C2 | semidirect |
| 4. #68721 | C2 | semidirect |
| 19. C2×#338 | D3 | semidirect |
| 219. C3 | #23723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83762 | 2 |
| C2×#5125 | 2 |
| C2×C3×#338 | 2 |
| #68721 | 2 |
| #23723 | 3 |