Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
650 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 142 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. #11724365 | C2 | semidirect |
| 3. #11724364 | C2 | semidirect |
| 4. C3×C4⋊PSU(3,𝔽2) | C2 | semidirect |
| 7. #11724154 | C2 | semidirect |
| 8. #11724153 | C2 | semidirect |
| 37. C4⋊PSU(3,𝔽2) | D3 | direct (N × H) |
| 50. D3×#157 | Q8 | semidirect |
| 51. C4×C3⋊(C3⋊D3) | Q8 | semidirect |
| 53. C32×C4×D3 | Q8 | semidirect |
| 54. #6289 | Q8 | semidirect |
| 56. D3×C3⋊Dic3 | Q8 | semidirect |
| 84. C3⋊#157 | C2×Q8 | semidirect |
| 87. C3×#157 | C2×Q8 | semidirect |
| 88. C33×C4 | C2×Q8 | semidirect |
| 89. C3⋊(C3⋊Dic3) | C2×Q8 | semidirect |
| 90. C3×C3⋊Dic3 | C2×Q8 | semidirect |
| 91. C32×Dic3 | C2×Q8 | semidirect |
| 130. C3⋊(C3⋊D3) | C4⋊Q8 | semidirect |
| 133. C32×D3 | C4⋊Q8 | semidirect |
| 169. #157 | D3×Q8 | semidirect |
| 173. C32×C4 | D3×Q8 | semidirect |
| 177. C3⋊Dic3 | D3×Q8 | semidirect |
| 189. C33 | C2×C4⋊Q8 | semidirect |
| 214. C4×D3 | PSU(3,𝔽2) | semidirect |
| 265. C3×C4 | C2×PSU(3,𝔽2) | semidirect |
| 273. Dic3 | C2×PSU(3,𝔽2) | semidirect |
| 276. C32 | D3×C4⋊Q8 | semidirect |
| 307. D3 | C4⋊PSU(3,𝔽2) | direct (N × H) |
| 322. C4 | D3×PSU(3,𝔽2) | semidirect |
| 325. 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 |
| #11724365 | 2 |
| #11724364 | 2 |
| C3×C4⋊PSU(3,𝔽2) | 2 |
| D3×C4⋊#157 | 2 |
| C4×D3×#157 | 2 |
| #11724154 | 2 |
| #11724153 | 2 |
| D3×#3777 | 2 |
| C2×C4⋊PSU(3,𝔽2) | 3 |
| D3×C4⋊Q8 | 9 |