Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
234 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 4. C8×PSU(3,𝔽2) | C3 | direct (N × H) |
| 15. C3×PSU(3,𝔽2) | C8 | direct (N × H) |
| 18. C33×C8 | Q8 | semidirect |
| 19. C3×C3⋊(C3⋊C8) | Q8 | semidirect |
| 37. PSU(3,𝔽2) | C3×C8 | direct (N × H) |
| 43. C32×C8 | C3×Q8 | semidirect |
| 44. C3⋊(C3⋊C8) | C3×Q8 | semidirect |
| 68. C33 | C8×Q8 | semidirect |
| 78. C3×C8 | PSU(3,𝔽2) | direct (N × H) |
| 103. C32 | C3×C8×Q8 | semidirect |
| 110. C8 | C3×PSU(3,𝔽2) | direct (N × H) |
| 125. C3 | C8×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 |
|---|---|
| C3×C4×PSU(3,𝔽2) | 2 |
| C3×C8×#157 | 2 |
| C3×#63744 | 2 |
| C8×PSU(3,𝔽2) | 3 |
| C3×C8×Q8 | 9 |