Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
782 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 782 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 1. C2×C3×#441 | C2 | semidirect |
| 4. #72074 | C2 | semidirect |
| 5. #71637 | C2 | semidirect |
| 6. #70593 | C2 | semidirect |
| 7. #70286 | C2 | semidirect |
| 8. #69841 | C2 | semidirect |
| 32. C2×#441 | D3 | semidirect |
| 308. C3 | #28179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#441 | 2 |
| #82441 | 2 |
| #78491 | 2 |
| #72074 | 2 |
| #71637 | 2 |
| #70593 | 2 |
| #70286 | 2 |
| #69841 | 2 |
| #28179 | 3 |