Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
400 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×C3×#330 | C2 | semidirect |
| 4. #71737 | C2 | semidirect |
| 6. #67662 | C2 | semidirect |
| 7. #67661 | C2 | semidirect |
| 39. C2×#330 | D3 | semidirect |
| 380. C3 | #9266 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83018 | 2 |
| #78481 | 2 |
| C2×C3×#330 | 2 |
| #71737 | 2 |
| #69799 | 2 |
| #67662 | 2 |
| #67661 | 2 |
| #9266 | 3 |