Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
666 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 666 conjugacy classes of subgroups — too many to draw. Only its 180 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⋊PSU(3,𝔽2) | C2 | semidirect |
| 3. C3×C4×PSU(3,𝔽2) | C2 | semidirect |
| 5. #11724148 | C2 | semidirect |
| 6. Dic3×PSU(3,𝔽2) | C2 | semidirect |
| 13. D3×PSU(3,𝔽2) | C4 | direct (N × H) |
| 28. C4×PSU(3,𝔽2) | D3 | direct (N × H) |
| 34. C3⋊PSU(3,𝔽2) | C2×C4 | semidirect |
| 35. C3×PSU(3,𝔽2) | C2×C4 | semidirect |
| 38. C4×C3⋊(C3⋊D3) | Q8 | semidirect |
| 40. C32×C4×D3 | Q8 | semidirect |
| 41. #6289 | Q8 | semidirect |
| 43. D3×C3⋊Dic3 | Q8 | semidirect |
| 68. C33×C4 | C2×Q8 | semidirect |
| 69. C3⋊(C3⋊Dic3) | C2×Q8 | semidirect |
| 70. C3×C3⋊Dic3 | C2×Q8 | semidirect |
| 71. C32×Dic3 | C2×Q8 | semidirect |
| 88. PSU(3,𝔽2) | C4×D3 | direct (N × H) |
| 104. C3⋊(C3⋊D3) | C4×Q8 | semidirect |
| 107. C32×D3 | C4×Q8 | semidirect |
| 140. C32×C4 | D3×Q8 | semidirect |
| 144. C3⋊Dic3 | D3×Q8 | semidirect |
| 154. C33 | C2×C4×Q8 | semidirect |
| 176. C4×D3 | PSU(3,𝔽2) | direct (N × H) |
| 220. C3×C4 | C2×PSU(3,𝔽2) | semidirect |
| 227. Dic3 | C2×PSU(3,𝔽2) | semidirect |
| 230. C32 | C4×D3×Q8 | semidirect |
| 257. D3 | C4×PSU(3,𝔽2) | direct (N × H) |
| 270. C4 | D3×PSU(3,𝔽2) | direct (N × H) |
| 273. C3 | C2×C4×PSU(3,𝔽2) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×PSU(3,𝔽2) | 2 |
| C4×C3⋊PSU(3,𝔽2) | 2 |
| C3×C4×PSU(3,𝔽2) | 2 |
| C4×D3×#157 | 2 |
| #11724148 | 2 |
| Dic3×PSU(3,𝔽2) | 2 |
| D3×#3777 | 2 |
| C2×C4×PSU(3,𝔽2) | 3 |
| C4×D3×Q8 | 9 |