Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
470 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 113 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×#1549 | C2 | semidirect |
| 3. #71790 | C2 | semidirect |
| 5. #70741 | C2 | semidirect |
| 7. #70491 | C2 | semidirect |
| 31. #1549 | D3 | semidirect |
| 295. C3 | #9812 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5088 | 2 |
| C3×#1549 | 2 |
| #71790 | 2 |
| #70774 | 2 |
| #70741 | 2 |
| #70521 | 2 |
| #70491 | 2 |
| #9812 | 3 |