Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
392 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 103 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. #70787 | C2 | semidirect |
| 5. #69863 | C2 | semidirect |
| 7. #69732 | C2 | semidirect |
| 38. C8×M16 | D3 | semidirect |
| 343. C3 | #9789 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4697 | 2 |
| C3×C8×M16 | 2 |
| #70787 | 2 |
| #70784 | 2 |
| #69863 | 2 |
| #69860 | 2 |
| #69732 | 2 |
| #9789 | 3 |