Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
294 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 178. C3 | #9609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#334 | 2 |
| #70420 | 2 |
| C4×#819 | 2 |
| #69726 | 2 |
| #67706 | 2 |
| #9609 | 3 |