Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
418 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 4. #67528 | C2 | semidirect |
| 8. C22×Dic12 | C4 | semidirect |
| 13. #5116 | C4 | semidirect |
| 16. C2×#818 | C4 | semidirect |
| 291. C3 | #11887 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5116 | 2 |
| C2×C3×C22⋊C16 | 2 |
| #71971 | 2 |
| #67528 | 2 |
| #11887 | 3 |