Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
526 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 403 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. Q8×C3⋊C16 | C2 | semidirect |
| 35. C2×C3×Q8 | C16 | semidirect |
| 73. C2×Q8 | C3⋊C16 | semidirect |
| 122. C3 | #33496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C8×Q8 | 2 |
| Q8×C3⋊C16 | 2 |
| #69744 | 2 |
| #33496 | 3 |