Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
382 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 131 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. #67718 | C2 | semidirect |
| 203. C3 | #11443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#424 | 2 |
| #71963 | 2 |
| #67718 | 2 |
| #11443 | 3 |