Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
620 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 113 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×#3165 | C2 | semidirect |
| 4. #71826 | C2 | semidirect |
| 5. #71775 | C2 | semidirect |
| 7. #67667 | C2 | semidirect |
| 31. #3165 | D3 | semidirect |
| 121. C3×M16 | SD16 | semidirect |
| 246. M16 | #215 | semidirect |
| 343. C3 | #10153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3165 | 2 |
| #83355 | 2 |
| C2×#5085 | 2 |
| #71826 | 2 |
| #71775 | 2 |
| #69876 | 2 |
| #67667 | 2 |
| #10153 | 3 |