Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
642 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 642 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. #83288 | C2 | semidirect |
| 3. C2×#4694 | C2 | semidirect |
| 4. C3×#1492 | C2 | semidirect |
| 5. #70521 | C2 | semidirect |
| 6. #70506 | C2 | semidirect |
| 7. #67656 | C2 | semidirect |
| 35. #1492 | D3 | semidirect |
| 148. #208 | D8 | semidirect |
| 370. C3 | #10168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83302 | 2 |
| #83288 | 2 |
| C2×#4694 | 2 |
| C3×#1492 | 2 |
| #70521 | 2 |
| #70506 | 2 |
| #67656 | 2 |
| #10168 | 3 |