Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
628 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 85 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×#3234 | C2 | semidirect |
| 3. #83067 | C2 | semidirect |
| 4. #71812 | C2 | semidirect |
| 5. #71735 | C2 | semidirect |
| 6. #70818 | C2 | semidirect |
| 7. #67748 | C2 | semidirect |
| 32. #3234 | D3 | semidirect |
| 372. C3 | #10089 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3234 | 2 |
| #83287 | 2 |
| #83067 | 2 |
| #71812 | 2 |
| #71735 | 2 |
| #70818 | 2 |
| #67748 | 2 |
| #10089 | 3 |