Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
244 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 71 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×#2183 | C2 | semidirect |
| 2. #70939 | C2 | semidirect |
| 4. #67560 | C2 | semidirect |
| 5. #67501 | C2 | semidirect |
| 19. #2183 | D3 | semidirect |
| 68. C3×C16 | SD16 | semidirect |
| 120. C16 | #215 | semidirect |
| 162. C3 | #12442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2183 | 2 |
| #70939 | 2 |
| #69060 | 2 |
| #67560 | 2 |
| #67501 | 2 |
| #12442 | 3 |