Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
444 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 444 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 |
|---|---|---|
| 2. C3×#1975 | C2 | semidirect |
| 3. C2×#4566 | C2 | semidirect |
| 4. C2×#4495 | C2 | semidirect |
| 5. C2×#4494 | C2 | semidirect |
| 6. #69825 | C2 | semidirect |
| 7. C2×#4466 | C2 | semidirect |
| 17. C2×#828 | C4 | semidirect |
| 18. C2×#826 | C4 | semidirect |
| 33. #1975 | D3 | semidirect |
| 138. C3⋊C16 | C22⋊C4 | semidirect |
| 338. C3 | #13249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5193 | 2 |
| C3×#1975 | 2 |
| C2×#4566 | 2 |
| C2×#4495 | 2 |
| C2×#4494 | 2 |
| #69825 | 2 |
| C2×#4466 | 2 |
| #13249 | 3 |