Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
478 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 131 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. #70780 | C2 | semidirect |
| 5. #69879 | C2 | semidirect |
| 7. #69730 | C2 | semidirect |
| 33. C8×M16 | D3 | semidirect |
| 295. C3 | #9800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4694 | 2 |
| C3×C8×M16 | 2 |
| #70780 | 2 |
| #70774 | 2 |
| #69879 | 2 |
| #69876 | 2 |
| #69730 | 2 |
| #9800 | 3 |