Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
754 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 153 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×#5070 | C2 | semidirect |
| 3. #71764 | C2 | semidirect |
| 4. #69771 | C2 | semidirect |
| 5. C3⋊#1273 | C2 | semidirect |
| 262. C3 | #10307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#493 | 2 |
| C2×#5070 | 2 |
| #71764 | 2 |
| #69771 | 2 |
| C3⋊#1273 | 2 |
| #10307 | 3 |