Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
450 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 450 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 |
|---|---|---|
| 4. #70779 | C2 | semidirect |
| 5. #70740 | C2 | semidirect |
| 6. #70516 | C2 | semidirect |
| 7. #70508 | C2 | semidirect |
| 291. C3 | #9769 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5070 | 2 |
| C3×#1545 | 2 |
| #71759 | 2 |
| #70779 | 2 |
| #70740 | 2 |
| #70516 | 2 |
| #70508 | 2 |
| #9769 | 3 |