Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
958 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×C3×#491 | C2 | semidirect |
| 3. C2×#5089 | C2 | semidirect |
| 4. C2×#4543 | C2 | semidirect |
| 5. #71251 | C2 | direct (N × H) |
| 6. C2×#4464 | C2 | semidirect |
| 18. C3×#491 | C22 | semidirect |
| 22. #5089 | C22 | semidirect |
| 26. #4543 | C22 | semidirect |
| 27. #4464 | C22 | semidirect |
| 29. C2×#491 | D3 | semidirect |
| 82. #491 | C2×D3 | semidirect |
| 274. C2×C3 | #1662 | semidirect |
| 292. C3 | C2×#1662 | semidirect |
| 294. C2 | #71251 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5700 | 2 |
| C2×C3×#491 | 2 |
| C2×#5089 | 2 |
| C2×#4543 | 2 |
| #71251 | 2 |
| C2×#4464 | 2 |
| C2×#1662 | 3 |