Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
610 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 125 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×#1965 | C2 | semidirect |
| 3. #71759 | C2 | semidirect |
| 4. #70502 | C2 | semidirect |
| 5. #70491 | C2 | semidirect |
| 6. #69876 | C2 | semidirect |
| 7. M16×C3⋊C8 | C2 | semidirect |
| 29. #1965 | D3 | semidirect |
| 115. C3×M16 | D8 | semidirect |
| 204. C3⋊C8 | #100 | semidirect |
| 235. M16 | #213 | semidirect |
| 330. C3 | #9802 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5073 | 2 |
| C3×#1965 | 2 |
| #71759 | 2 |
| #70502 | 2 |
| #70491 | 2 |
| #69876 | 2 |
| M16×C3⋊C8 | 2 |
| #9802 | 3 |