Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
216 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 79 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. #69056 | C2 | semidirect |
| 3. C3×C8×C16 | C2 | semidirect |
| 4. #67502 | C2 | semidirect |
| 5. #67441 | C2 | semidirect |
| 21. C8×C16 | D3 | semidirect |
| 33. Dic24 | C8 | semidirect |
| 34. #800 | C8 | semidirect |
| 35. D48 | C8 | semidirect |
| 139. C3 | #12046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #69067 | 2 |
| #69056 | 2 |
| C3×C8×C16 | 2 |
| #67502 | 2 |
| #67441 | 2 |
| #12046 | 3 |