Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1378 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 1378 conjugacy classes of subgroups — too many to draw. Only its 259 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 |
|---|---|---|
| 3. C2×#5116 | C2 | semidirect |
| 4. #71989 | C2 | semidirect |
| 5. #71971 | C2 | semidirect |
| 214. C3 | #32934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#131 | 2 |
| #84094 | 2 |
| C2×#5116 | 2 |
| #71989 | 2 |
| #71971 | 2 |
| #32934 | 3 |