Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
630 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 1. C2×D3×PSU(3,𝔽2) | C2 | semidirect |
| 2. #11724364 | C2 | semidirect |
| 3. C4×C3⋊PSU(3,𝔽2) | C2 | semidirect |
| 4. C3×C4⋊PSU(3,𝔽2) | C2 | semidirect |
| 7. #11724151 | C2 | semidirect |
| 8. #11724149 | C2 | semidirect |
| 33. C4⋊PSU(3,𝔽2) | D3 | semidirect |
| 43. C3⋊PSU(3,𝔽2) | D4 | semidirect |
| 47. C4⋊(C3⋊(C3⋊D3)) | Q8 | semidirect |
| 49. C32×D12 | Q8 | semidirect |
| 50. #6291 | Q8 | semidirect |
| 70. C2×C3⋊(C3⋊D3) | C2×Q8 | semidirect |
| 72. C2×C32×D3 | C2×Q8 | semidirect |
| 81. C33×C4 | C2×Q8 | semidirect |
| 82. C3×C3⋊Dic3 | C2×Q8 | semidirect |
| 156. C32×C4 | D3×Q8 | semidirect |
| 157. C3⋊Dic3 | D3×Q8 | semidirect |
| 167. C33 | D4×Q8 | semidirect |
| 184. D12 | PSU(3,𝔽2) | semidirect |
| 229. C2×D3 | C2×PSU(3,𝔽2) | semidirect |
| 236. C3×C4 | C2×PSU(3,𝔽2) | semidirect |
| 243. C32 | #5727 | semidirect |
| 284. C4 | D3×PSU(3,𝔽2) | semidirect |
| 287. C3 | D4×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 |
| #11724364 | 2 |
| C4×C3⋊PSU(3,𝔽2) | 2 |
| C3×C4⋊PSU(3,𝔽2) | 2 |
| #11724259 | 2 |
| D12×#157 | 2 |
| #11724151 | 2 |
| #11724149 | 2 |
| D4×PSU(3,𝔽2) | 3 |
| #5727 | 9 |