Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
614 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 105 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×#3037 | C2 | semidirect |
| 3. C2×#5027 | C2 | semidirect |
| 4. #71800 | C2 | semidirect |
| 5. #71624 | C2 | semidirect |
| 6. #70502 | C2 | semidirect |
| 7. #67714 | C2 | semidirect |
| 33. #3037 | D3 | semidirect |
| 121. C2×C3×Q8 | D8 | semidirect |
| 280. C2×Q8 | #213 | semidirect |
| 435. C3 | #10177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3037 | 2 |
| #83302 | 2 |
| C2×#5027 | 2 |
| #71800 | 2 |
| #71624 | 2 |
| #70502 | 2 |
| #67714 | 2 |
| #10177 | 3 |