Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
432 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 93 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×#360 | C2 | semidirect |
| 3. #72078 | C2 | semidirect |
| 4. C2×#4514 | C2 | semidirect |
| 5. #71428 | C2 | semidirect |
| 6. #70578 | C2 | semidirect |
| 7. #67721 | C2 | semidirect |
| 32. C2×#360 | D3 | semidirect |
| 67. C3×M32 | D4 | semidirect |
| 194. M32 | #67 | semidirect |
| 407. C3 | #13386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83915 | 2 |
| C2×C3×#360 | 2 |
| #72078 | 2 |
| C2×#4514 | 2 |
| #71428 | 2 |
| #70578 | 2 |
| #67721 | 2 |
| #13386 | 3 |