Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
354 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 93 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. C3×#1571 | C2 | semidirect |
| 4. #70494 | C2 | semidirect |
| 5. #70446 | C2 | semidirect |
| 7. #67737 | C2 | semidirect |
| 25. #1571 | D3 | semidirect |
| 253. C3 | #10667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#1571 | 2 |
| #70758 | 2 |
| #70513 | 2 |
| #70494 | 2 |
| #70446 | 2 |
| #70426 | 2 |
| #67737 | 2 |
| #10667 | 3 |