Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
476 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 81 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×#3142 | C2 | semidirect |
| 3. #83019 | C2 | semidirect |
| 4. #71803 | C2 | semidirect |
| 5. #71737 | C2 | semidirect |
| 6. #69853 | C2 | semidirect |
| 7. #67670 | C2 | semidirect |
| 36. #3142 | D3 | semidirect |
| 372. C3 | #10122 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3142 | 2 |
| #83308 | 2 |
| #83019 | 2 |
| #71803 | 2 |
| #71737 | 2 |
| #69853 | 2 |
| #67670 | 2 |
| #10122 | 3 |