Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2310 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2310 conjugacy classes of subgroups — too many to draw. Only its 747 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. C22×#870 | C2 | semidirect |
| 3. C22×#835 | C2 | semidirect |
| 5. C2×#5056 | C2 | direct (N × H) |
| 6. C22×C4×C3⋊C8 | C2 | semidirect |
| 18. C2×#870 | C22 | semidirect |
| 19. C2×#835 | C22 | semidirect |
| 21. #5056 | C22 | direct (N × H) |
| 22. C2×C4×C3⋊C8 | C22 | semidirect |
| 51. #870 | C23 | semidirect |
| 52. #835 | C23 | semidirect |
| 54. C4×C3⋊C8 | C23 | semidirect |
| 179. C22×C3 | #488 | semidirect |
| 211. C2×C3 | C2×#488 | semidirect |
| 217. C22 | #5056 | direct (N × H) |
| 226. C3 | C22×#488 | semidirect |
| 228. C2 | C2×#5056 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#124 | 2 |
| C22×#870 | 2 |
| C22×#835 | 2 |
| C22×#832 | 2 |
| C2×#5056 | 2 |
| C22×C4×C3⋊C8 | 2 |
| C22×#488 | 3 |