Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
610 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 139 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. #70774 | C2 | semidirect |
| 4. #69876 | C2 | semidirect |
| 5. #69731 | C2 | semidirect |
| 25. C8×M16 | D3 | semidirect |
| 80. C3×M16 | D8 | semidirect |
| 144. C3×C8 | #100 | semidirect |
| 164. M16 | D24 | semidirect |
| 216. C8 | #823 | semidirect |
| 237. C3 | #9802 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4695 | 2 |
| C3×C8×M16 | 2 |
| #70774 | 2 |
| #69876 | 2 |
| #69731 | 2 |
| #9802 | 3 |