Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
830 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 830 conjugacy classes of subgroups — too many to draw. Only its 331 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. #69438 | C2 | semidirect |
| 95. C3 | #20773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#376 | 2 |
| #71527 | 2 |
| #69438 | 2 |
| #20773 | 3 |