Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
666 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 666 conjugacy classes of subgroups — too many to draw. Only its 228 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 |
|---|---|---|
| 4. Dic3×PSU(3,𝔽2) | C2 | direct (N × H) |
| 8. C2×C3×PSU(3,𝔽2) | C4 | semidirect |
| 22. C3×PSU(3,𝔽2) | C2×C4 | semidirect |
| 23. C2×C3⋊(C3⋊Dic3) | Q8 | semidirect |
| 24. C2×C32×Dic3 | Q8 | semidirect |
| 25. Dic3×C3⋊D3 | Q8 | semidirect |
| 30. C2×PSU(3,𝔽2) | Dic3 | direct (N × H) |
| 43. C3⋊(C3⋊Dic3) | C2×Q8 | semidirect |
| 44. C32×Dic3 | C2×Q8 | semidirect |
| 55. PSU(3,𝔽2) | C2×Dic3 | direct (N × H) |
| 66. C2×C33 | C4×Q8 | semidirect |
| 68. C3×C3⋊D3 | C4×Q8 | semidirect |
| 101. C33 | C2×C4×Q8 | semidirect |
| 115. C2×Dic3 | PSU(3,𝔽2) | direct (N × H) |
| 122. C2×C32 | Q8×Dic3 | semidirect |
| 124. C3⋊D3 | Q8×Dic3 | semidirect |
| 154. Dic3 | C2×PSU(3,𝔽2) | direct (N × H) |
| 157. C32 | C2×Q8×Dic3 | semidirect |
| 175. C2×C3 | C4×PSU(3,𝔽2) | semidirect |
| 191. C3 | C2×C4×PSU(3,𝔽2) | semidirect |
| 195. C2 | Dic3×PSU(3,𝔽2) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×PSU(3,𝔽2) | 2 |
| C2×#88946 | 2 |
| C2×Dic3×#157 | 2 |
| Dic3×PSU(3,𝔽2) | 2 |
| C2×C4×PSU(3,𝔽2) | 3 |
| C2×Q8×Dic3 | 9 |