Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1102 conjugacy classes of subgroups; only the 391 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 391 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. #83789 | C2 | semidirect |
| 3. #83780 | C2 | semidirect |
| 4. #72081 | C2 | semidirect |
| 5. C2×#4565 | C2 | semidirect |
| 222. C3 | #33393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#578 | 2 |
| #83789 | 2 |
| #83780 | 2 |
| #72081 | 2 |
| C2×#4565 | 2 |
| #33393 | 3 |