Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
560 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 176 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. C4⋊(C3⋊(C3⋊Dic3)) | C2 | semidirect |
| 3. C3×C4⋊(C3⋊Dic3) | C2 | semidirect |
| 5. Dic3×C3⋊Dic3 | C2 | semidirect |
| 13. C32×C4×D3 | C4 | semidirect |
| 20. C4⋊(C3⋊Dic3) | D3 | semidirect |
| 48. C3×C4×D3 | Dic3 | semidirect |
| 84. C33 | #117 | semidirect |
| 98. C4×D3 | C3⋊Dic3 | semidirect |
| 135. C32 | #892 | semidirect |
| 136. C32 | #926 | semidirect |
| 163. C3 | #63841 | semidirect |
| 164. C3 | #64135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4×D3 | 2 |
| C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| C3×C4⋊(C3⋊Dic3) | 2 |
| (C2×D3)⋊(C3⋊Dic3) | 2 |
| Dic3×C3⋊Dic3 | 2 |
| #64135 | 3 |
| #63841 | 3 |