Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
380 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 75 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. #70825 | C2 | semidirect |
| 5. #69862 | C2 | semidirect |
| 6. #69851 | C2 | semidirect |
| 7. #67754 | C2 | semidirect |
| 355. C3 | #10498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #82949 | 2 |
| C3×#1527 | 2 |
| #71727 | 2 |
| #70825 | 2 |
| #69862 | 2 |
| #69851 | 2 |
| #67754 | 2 |
| #10498 | 3 |