Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
602 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 127 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×#1566 | C2 | semidirect |
| 3. #70521 | C2 | semidirect |
| 4. #70502 | C2 | semidirect |
| 5. #69725 | C2 | semidirect |
| 23. #1566 | D3 | semidirect |
| 141. C3×C8 | #100 | semidirect |
| 211. C8 | #823 | semidirect |
| 231. C3 | #9811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4695 | 2 |
| C3×#1566 | 2 |
| #70521 | 2 |
| #70502 | 2 |
| #69725 | 2 |
| #9811 | 3 |