Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
472 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. C2×#4517 | C2 | semidirect |
| 5. #69824 | C2 | semidirect |
| 6. C3×#1375 | C2 | semidirect |
| 7. #67816 | C2 | semidirect |
| 22. C2×Dic24 | C4 | semidirect |
| 23. C2×#800 | C4 | semidirect |
| 34. #1375 | D3 | semidirect |
| 333. C3 | #13039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4909 | 2 |
| C2×#4717 | 2 |
| C2×#4518 | 2 |
| C2×#4517 | 2 |
| #69824 | 2 |
| C3×#1375 | 2 |
| #67816 | 2 |
| #13039 | 3 |