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 |
| 5. Dic3×C3⋊Dic3 | C2 | semidirect |
| 11. C4×C3⋊(C3⋊D3) | C4 | semidirect |
| 19. C4⋊(C3⋊Dic3) | D3 | semidirect |
| 22. C3×C4⋊Dic3 | D3 | semidirect |
| 63. C4⋊Dic3 | C3⋊D3 | semidirect |
| 89. C33 | #117 | semidirect |
| 146. C32 | #892 | semidirect |
| 147. C32 | #892 | semidirect |
| 175. C3 | #63849 | semidirect |
| 176. C3 | #64101 | 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 |
| #88804 | 2 |
| Dic3×C3⋊Dic3 | 2 |
| #64101 | 3 |
| #63849 | 3 |