Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
620 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 107 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. #83341 | C2 | semidirect |
| 4. C3×#1493 | C2 | semidirect |
| 6. #70508 | C2 | semidirect |
| 7. #67656 | C2 | semidirect |
| 35. #1493 | D3 | semidirect |
| 142. #208 | SD16 | semidirect |
| 343. C3 | #10153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83355 | 2 |
| #83341 | 2 |
| C2×#4693 | 2 |
| C3×#1493 | 2 |
| #70521 | 2 |
| #70508 | 2 |
| #67656 | 2 |
| #10153 | 3 |