Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
190 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 54 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. C2×C3×PSU(3,𝔽2) | C2 | semidirect |
| 4. C3×#3777 | C2 | semidirect |
| 5. C3×#3777 | C2 | semidirect |
| 6. C22⋊PSU(3,𝔽2) | C3 | direct (N × H) |
| 15. C2×PSU(3,𝔽2) | C2×C3 | semidirect |
| 17. #3777 | C2×C3 | semidirect |
| 18. #3777 | C2×C3 | semidirect |
| 19. C22×C33 | Q8 | semidirect |
| 22. C2×C3×C3⋊D3 | Q8 | semidirect |
| 49. C22×C32 | C3×Q8 | semidirect |
| 52. C2×C3⋊D3 | C3×Q8 | semidirect |
| 63. C33 | C22⋊Q8 | semidirect |
| 95. C22×C3 | PSU(3,𝔽2) | semidirect |
| 106. C32 | C3×C22⋊Q8 | semidirect |
| 130. C22 | C3×PSU(3,𝔽2) | semidirect |
| 137. C3 | C22⋊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×#157 | 2 |
| C2×C3×PSU(3,𝔽2) | 2 |
| C3×C22⋊#157 | 2 |
| C3×#3777 | 2 |
| C22⋊PSU(3,𝔽2) | 3 |
| C3×C22⋊Q8 | 9 |