Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
694 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 163 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×#1834 | C2 | semidirect |
| 3. C2×#4454 | C2 | semidirect |
| 4. #69580 | C2 | semidirect |
| 5. #69580 | C2 | semidirect |
| 16. #4695 | C4 | semidirect |
| 22. #1834 | D3 | semidirect |
| 90. C2×C3⋊C8 | D8 | semidirect |
| 252. C3 | #9832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4695 | 2 |
| C3×#1834 | 2 |
| C2×#4454 | 2 |
| #69580 | 2 |
| #9832 | 3 |