Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
474 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 135 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×#3407 | C2 | semidirect |
| 3. #72007 | C2 | semidirect |
| 4. #71438 | C2 | semidirect |
| 5. #67810 | C2 | semidirect |
| 22. #3407 | D3 | semidirect |
| 50. C3×M32 | D4 | semidirect |
| 140. M32 | #67 | semidirect |
| 279. C3 | #12982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3407 | 2 |
| #83786 | 2 |
| #72007 | 2 |
| #71438 | 2 |
| #67810 | 2 |
| #12982 | 3 |