Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
320 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 117 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. C4⋊((C3⋊Dic3)⋊C3) | C2 | semidirect |
| 4. C4×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 5. #64135 | C3 | semidirect |
| 8. C2×C4×H(3,𝔽3) | C4 | semidirect |
| 16. C4⋊(C3⋊Dic3) | C2×C3 | semidirect |
| 17. C4×C3⋊Dic3 | C2×C3 | semidirect |
| 36. C2×C32×C4 | Dic3 | semidirect |
| 37. C2×C32×C4 | C3×C4 | semidirect |
| 78. H(3,𝔽3) | #117 | semidirect |
| 135. C32 | #926 | semidirect |
| 136. C32 | C3×#117 | semidirect |
| 139. C2×C4 | (C3⋊Dic3)⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×H(3,𝔽3) | 2 |
| #3757⋊C3 | 2 |
| C4⋊((C3⋊Dic3)⋊C3) | 2 |
| C4×(C3⋊Dic3)⋊C3 | 2 |
| #64135 | 3 |
| C3×#926 | 3 |