Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
726 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 207 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. #71764 | C2 | semidirect |
| 3. #69765 | C2 | semidirect |
| 4. C2×C8×C3⋊C8 | C2 | semidirect |
| 9. C3×#493 | C4 | semidirect |
| 42. #493 | Dic3 | semidirect |
| 72. C2×C3⋊C8 | D8 | semidirect |
| 112. C3×C8 | #102 | semidirect |
| 174. C8 | #832 | semidirect |
| 196. C3 | #9824 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#493 | 2 |
| #71764 | 2 |
| #69765 | 2 |
| C2×C8×C3⋊C8 | 2 |
| #9824 | 3 |