Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
320 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 77 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×#634⋊C3 | C2 | semidirect |
| 3. #3757⋊C3 | C2 | semidirect |
| 4. C4×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 5. #64145 | C3 | semidirect |
| 16. C2×#634 | C2×C3 | semidirect |
| 18. #3757 | C2×C3 | semidirect |
| 19. C4×C3⋊Dic3 | C2×C3 | semidirect |
| 79. H(3,𝔽3) | #124 | semidirect |
| 137. C32 | #936 | semidirect |
| 138. C32 | C3×#124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×H(3,𝔽3) | 2 |
| C2×#634⋊C3 | 2 |
| #3757⋊C3 | 2 |
| C4×(C3⋊Dic3)⋊C3 | 2 |
| #64145 | 3 |
| C3×#936 | 3 |