Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
442 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 104 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×C32×Dic6 | C2 | semidirect |
| 3. C32×C4×Dic3 | C2 | semidirect |
| 4. C3×#3722 | C2 | semidirect |
| 7. #63864 | C3 | direct (N × H) |
| 20. C2×C3×Dic6 | D3 | semidirect |
| 21. C2×C3×Dic6 | C2×C3 | semidirect |
| 26. C3×C4×Dic3 | D3 | semidirect |
| 27. C3×C4×Dic3 | C2×C3 | semidirect |
| 28. #3722 | C2×C3 | semidirect |
| 75. C2×Dic6 | C3×D3 | semidirect |
| 82. C4×Dic3 | C3×D3 | semidirect |
| 114. C33 | #124 | semidirect |
| 198. C32 | #875 | semidirect |
| 199. C32 | #947 | semidirect |
| 200. C32 | C3×#124 | semidirect |
| 235. C3 | #63864 | direct (N × H) |
| 236. C3 | C3×#875 | semidirect |
| 237. C3 | C3×#947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4⋊(C3⋊D3) | 2 |
| C2×C32×Dic6 | 2 |
| C32×C4×Dic3 | 2 |
| C3×#3722 | 2 |
| C3×#947 | 3 |
| C3×#875 | 3 |
| #63864 | 3 |