Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
672 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 136 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. C3×C4×C3⋊Dic3 | C2 | semidirect |
| 3. C32×C4×Dic3 | C2 | semidirect |
| 4. #88806 | C2 | semidirect |
| 11. C4×C3⋊(C3⋊D3) | C4 | semidirect |
| 20. C4×C3⋊Dic3 | D3 | semidirect |
| 22. C3×C4×Dic3 | D3 | semidirect |
| 63. C4×Dic3 | C3⋊D3 | semidirect |
| 84. C33 | #117 | semidirect |
| 135. C32 | #872 | semidirect |
| 136. C32 | #872 | semidirect |
| 160. C3 | #63874 | semidirect |
| 161. C3 | #64081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C3⋊(C3⋊D3) | 2 |
| C3×C4×C3⋊Dic3 | 2 |
| C32×C4×Dic3 | 2 |
| #88806 | 2 |
| #88804 | 2 |
| #64081 | 3 |
| #63874 | 3 |