Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
460 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 152 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 |
|---|---|---|
| 2. C2×C3⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 3. C3×#3748 | C2 | semidirect |
| 4. #88786 | C2 | semidirect |
| 5. D3×C3⋊(C3⋊C8) | C2 | semidirect |
| 19. #3748 | D3 | semidirect |
| 81. C33 | #131 | semidirect |
| 128. C32 | #907 | semidirect |
| 129. C32 | #948 | semidirect |
| 152. C3 | #63815 | semidirect |
| 153. C3 | #64157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#235 | 2 |
| C2×C3⋊(C3⋊(C3⋊C8)) | 2 |
| C3×#3748 | 2 |
| #88786 | 2 |
| D3×C3⋊(C3⋊C8) | 2 |
| #64157 | 3 |
| #63815 | 3 |