Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
530 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. C3×#1960 | C2 | semidirect |
| 4. #71788 | C2 | semidirect |
| 6. #67659 | C2 | semidirect |
| 7. #67630 | C2 | semidirect |
| 16. #5089 | C4 | semidirect |
| 34. #1960 | D3 | semidirect |
| 46. C3×C4⋊Q8 | C2×C4 | semidirect |
| 82. #803 | C2×C4 | semidirect |
| 172. C4⋊Q8 | C4×D3 | semidirect |
| 424. C3 | #8999 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5089 | 2 |
| #74230 | 2 |
| C3×#1960 | 2 |
| #71788 | 2 |
| C2×#4464 | 2 |
| #67659 | 2 |
| #67630 | 2 |
| #8999 | 3 |