Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
470 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 111 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. #82436 | C2 | semidirect |
| 3. C3×#1805 | C2 | semidirect |
| 6. #67707 | C2 | semidirect |
| 7. #67631 | C2 | semidirect |
| 15. #5031 | C4 | semidirect |
| 17. #5027 | C4 | semidirect |
| 30. #1805 | D3 | semidirect |
| 360. C3 | #9310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #82441 | 2 |
| #82436 | 2 |
| C3×#1805 | 2 |
| #70426 | 2 |
| #69545 | 2 |
| #67707 | 2 |
| #67631 | 2 |
| #9310 | 3 |