Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
482 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 111 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×C8×M16 | C2 | semidirect |
| 3. #70784 | C2 | semidirect |
| 4. #69860 | C2 | semidirect |
| 5. #69732 | C2 | semidirect |
| 29. C8×M16 | D3 | semidirect |
| 285. C3 | #9787 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4696 | 2 |
| C3×C8×M16 | 2 |
| #70784 | 2 |
| #69860 | 2 |
| #69732 | 2 |
| #9787 | 3 |