Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
300 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 99 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×#2110 | C2 | semidirect |
| 4. #71421 | C2 | semidirect |
| 6. #67814 | C2 | semidirect |
| 7. #67671 | C2 | semidirect |
| 27. #2110 | D3 | semidirect |
| 269. C3 | #13126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2110 | 2 |
| #71437 | 2 |
| C2×#4515 | 2 |
| #71421 | 2 |
| #69898 | 2 |
| #67814 | 2 |
| #67671 | 2 |
| #13126 | 3 |