Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
810 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 810 conjugacy classes of subgroups — too many to draw. Only its 148 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. C22×C3×PSU(3,𝔽2) | C2 | semidirect |
| 3. C2×#88946 | C2 | semidirect |
| 4. C2×#88945 | C2 | semidirect |
| 6. #11724149 | C2 | direct (N × H) |
| 14. C2×C3×PSU(3,𝔽2) | C22 | semidirect |
| 17. #88946 | C22 | semidirect |
| 18. #88945 | C22 | semidirect |
| 21. C22×PSU(3,𝔽2) | D3 | semidirect |
| 26. C22×C3⋊(C3⋊D3) | Q8 | semidirect |
| 28. C22×C32×D3 | Q8 | semidirect |
| 31. C2×D3×C3⋊D3 | Q8 | semidirect |
| 53. C2×PSU(3,𝔽2) | C2×D3 | semidirect |
| 59. C2×C3⋊(C3⋊D3) | C2×Q8 | semidirect |
| 65. C2×C32×D3 | C2×Q8 | semidirect |
| 105. C2×C33 | C22⋊Q8 | semidirect |
| 108. C3×C3⋊D3 | C22⋊Q8 | semidirect |
| 162. C33 | C2×C22⋊Q8 | semidirect |
| 177. C22×D3 | PSU(3,𝔽2) | semidirect |
| 193. C2×C32 | #946 | semidirect |
| 198. C3⋊D3 | #946 | semidirect |
| 243. C2×D3 | C2×PSU(3,𝔽2) | semidirect |
| 250. C32 | C2×#946 | semidirect |
| 276. C2×C3 | C22⋊PSU(3,𝔽2) | semidirect |
| 303. C3 | C2×C22⋊PSU(3,𝔽2) | semidirect |
| 309. C2 | #11724149 | 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 |
| C22×D3×#157 | 2 |
| C2×#88946 | 2 |
| C2×#88945 | 2 |
| C2×(C2×D3)⋊#157 | 2 |
| #11724149 | 2 |
| C2×C22⋊PSU(3,𝔽2) | 3 |
| C2×#946 | 9 |