Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
202 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 1. C3×#2252 | C2 | semidirect |
| 3. #67577 | C2 | semidirect |
| 4. C4×C3⋊C32 | C2 | semidirect |
| 14. #2252 | D3 | semidirect |
| 126. C3 | #13719 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2252 | 2 |
| #69060 | 2 |
| #67577 | 2 |
| C4×C3⋊C32 | 2 |
| #13719 | 3 |