Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
406 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 123 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. #72007 | C2 | semidirect |
| 3. C2×#4561 | C2 | semidirect |
| 4. #69884 | C2 | semidirect |
| 5. #69882 | C2 | semidirect |
| 218. C3 | #13199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2955 | 2 |
| #72007 | 2 |
| C2×#4561 | 2 |
| #69884 | 2 |
| #69882 | 2 |
| #13199 | 3 |