Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
908 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 407 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. #68717 | C2 | semidirect |
| 10. Dic3×M16 | C4 | semidirect |
| 11. #5101 | C4 | semidirect |
| 34. #815 | C2×C4 | semidirect |
| 35. C8×Dic3 | C2×C4 | semidirect |
| 166. C3 | #20370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83747 | 2 |
| C2×C3×#338 | 2 |
| C2×#4557 | 2 |
| #68717 | 2 |
| #20370 | 3 |