Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
7134 conjugacy classes of subgroups; only the 1771 normal subgroups are shown.
This group has 7134 conjugacy classes of subgroups — too many to draw. Only its 1771 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. C23×#208 | C2 | semidirect |
| 3. C22×#833 | C2 | direct (N × H) |
| 12. C22×#208 | C22 | semidirect |
| 14. C2×#833 | C22 | direct (N × H) |
| 34. C2×#208 | C23 | semidirect |
| 36. #833 | C23 | direct (N × H) |
| 70. #208 | C24 | semidirect |
| 98. C23×C3 | #100 | semidirect |
| 143. C22×C3 | C2×#100 | semidirect |
| 156. C23 | #833 | direct (N × H) |
| 173. C2×C3 | C22×#100 | semidirect |
| 181. C22 | C2×#833 | direct (N × H) |
| 187. C3 | C23×#100 | semidirect |
| 191. C2 | C22×#833 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C3×D4 | 2 |
| C23×#208 | 2 |
| C22×#833 | 2 |
| C23×#100 | 3 |